For Mu ( 0 , 0 , 0 , 0 ) and Lambda ( 0 , 0 , 0 , 0 ) That's Mu ( 0 , 0 , 0 , 0 ) and Lambda ( 0 , 0 , 0 , 0 ) in Root notation. l(Lambda) = 0; l(Mu) = 0 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 1 Rank = 1 For Mu ( 0 , 0 , 0 , 0 ) and Lambda ( 3 , 0 , 0 , 3 ) That's Mu ( 0 , 0 , 0 , 0 ) and Lambda ( 3 , 3 , 3 , 3 ) in Root notation. l(Lambda) = 1; l(Mu) = 0 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 20 Rank = 19 For Mu ( 3 , 0 , 0 , 3 ) and Lambda ( 3 , 0 , 0 , 3 ) That's Mu ( 3 , 3 , 3 , 3 ) and Lambda ( 3 , 3 , 3 , 3 ) in Root notation. l(Lambda) = 1; l(Mu) = 1 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 1 Rank = 1 For Mu ( 0 , 0 , 0 , 0 ) and Lambda ( 4 , 0 , 1 , 2 ) That's Mu ( 0 , 0 , 0 , 0 ) and Lambda ( 4 , 4 , 4 , 3 ) in Root notation. l(Lambda) = 2; l(Mu) = 0 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 45 Rank = 26 For Mu ( 3 , 0 , 0 , 3 ) and Lambda ( 4 , 0 , 1 , 2 ) That's Mu ( 3 , 3 , 3 , 3 ) and Lambda ( 4 , 4 , 4 , 3 ) in Root notation. l(Lambda) = 2; l(Mu) = 1 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 3 Rank = 2 For Mu ( 4 , 0 , 1 , 2 ) and Lambda ( 4 , 0 , 1 , 2 ) That's Mu ( 4 , 4 , 4 , 3 ) and Lambda ( 4 , 4 , 4 , 3 ) in Root notation. l(Lambda) = 2; l(Mu) = 2 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 1 Rank = 1 For Mu ( 0 , 0 , 0 , 0 ) and Lambda ( 2 , 1 , 0 , 4 ) That's Mu ( 0 , 0 , 0 , 0 ) and Lambda ( 3 , 4 , 4 , 4 ) in Root notation. l(Lambda) = 2; l(Mu) = 0 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 45 Rank = 26 For Mu ( 3 , 0 , 0 , 3 ) and Lambda ( 2 , 1 , 0 , 4 ) That's Mu ( 3 , 3 , 3 , 3 ) and Lambda ( 3 , 4 , 4 , 4 ) in Root notation. l(Lambda) = 2; l(Mu) = 1 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 3 Rank = 2 For Mu ( 2 , 1 , 0 , 4 ) and Lambda ( 2 , 1 , 0 , 4 ) That's Mu ( 3 , 4 , 4 , 4 ) and Lambda ( 3 , 4 , 4 , 4 ) in Root notation. l(Lambda) = 2; l(Mu) = 2 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 1 Rank = 1 For Mu ( 0 , 0 , 0 , 0 ) and Lambda ( 5 , 1 , 0 , 2 ) That's Mu ( 0 , 0 , 0 , 0 ) and Lambda ( 5 , 5 , 4 , 3 ) in Root notation. l(Lambda) = 3; l(Mu) = 0 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 36 Rank = 10 For Mu ( 3 , 0 , 0 , 3 ) and Lambda ( 5 , 1 , 0 , 2 ) That's Mu ( 3 , 3 , 3 , 3 ) and Lambda ( 5 , 5 , 4 , 3 ) in Root notation. l(Lambda) = 3; l(Mu) = 1 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 3 Rank = 1 For Mu ( 4 , 0 , 1 , 2 ) and Lambda ( 5 , 1 , 0 , 2 ) That's Mu ( 4 , 4 , 4 , 3 ) and Lambda ( 5 , 5 , 4 , 3 ) in Root notation. l(Lambda) = 3; l(Mu) = 2 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 2 Rank = 1 For Mu ( 5 , 1 , 0 , 2 ) and Lambda ( 5 , 1 , 0 , 2 ) That's Mu ( 5 , 5 , 4 , 3 ) and Lambda ( 5 , 5 , 4 , 3 ) in Root notation. l(Lambda) = 3; l(Mu) = 3 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 1 Rank = 1 For Mu ( 0 , 0 , 0 , 0 ) and Lambda ( 3 , 1 , 1 , 3 ) That's Mu ( 0 , 0 , 0 , 0 ) and Lambda ( 4 , 5 , 5 , 4 ) in Root notation. l(Lambda) = 3; l(Mu) = 0 P(Mu,Lambda) = ( +1 t^0 +1 t^2 ) Weyl(Mu, Lambda) = 136 Rank = 64 For Mu ( 3 , 0 , 0 , 3 ) and Lambda ( 3 , 1 , 1 , 3 ) That's Mu ( 3 , 3 , 3 , 3 ) and Lambda ( 4 , 5 , 5 , 4 ) in Root notation. l(Lambda) = 3; l(Mu) = 1 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 14 Rank = 9 For Mu ( 4 , 0 , 1 , 2 ) and Lambda ( 3 , 1 , 1 , 3 ) That's Mu ( 4 , 4 , 4 , 3 ) and Lambda ( 4 , 5 , 5 , 4 ) in Root notation. l(Lambda) = 3; l(Mu) = 2 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 4 Rank = 3 For Mu ( 2 , 1 , 0 , 4 ) and Lambda ( 3 , 1 , 1 , 3 ) That's Mu ( 3 , 4 , 4 , 4 ) and Lambda ( 4 , 5 , 5 , 4 ) in Root notation. l(Lambda) = 3; l(Mu) = 2 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 4 Rank = 3 For Mu ( 3 , 1 , 1 , 3 ) and Lambda ( 3 , 1 , 1 , 3 ) That's Mu ( 4 , 5 , 5 , 4 ) and Lambda ( 4 , 5 , 5 , 4 ) in Root notation. l(Lambda) = 3; l(Mu) = 3 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 1 Rank = 1 For Mu ( 0 , 0 , 0 , 0 ) and Lambda ( 2 , 0 , 1 , 5 ) That's Mu ( 0 , 0 , 0 , 0 ) and Lambda ( 3 , 4 , 5 , 5 ) in Root notation. l(Lambda) = 3; l(Mu) = 0 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 36 Rank = 10 For Mu ( 3 , 0 , 0 , 3 ) and Lambda ( 2 , 0 , 1 , 5 ) That's Mu ( 3 , 3 , 3 , 3 ) and Lambda ( 3 , 4 , 5 , 5 ) in Root notation. l(Lambda) = 3; l(Mu) = 1 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 3 Rank = 1 For Mu ( 2 , 1 , 0 , 4 ) and Lambda ( 2 , 0 , 1 , 5 ) That's Mu ( 3 , 4 , 4 , 4 ) and Lambda ( 3 , 4 , 5 , 5 ) in Root notation. l(Lambda) = 3; l(Mu) = 2 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 2 Rank = 1 For Mu ( 2 , 0 , 1 , 5 ) and Lambda ( 2 , 0 , 1 , 5 ) That's Mu ( 3 , 4 , 5 , 5 ) and Lambda ( 3 , 4 , 5 , 5 ) in Root notation. l(Lambda) = 3; l(Mu) = 3 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 1 Rank = 1 For Mu ( 0 , 0 , 0 , 0 ) and Lambda ( 4 , 2 , 0 , 3 ) That's Mu ( 0 , 0 , 0 , 0 ) and Lambda ( 5 , 6 , 5 , 4 ) in Root notation. l(Lambda) = 4; l(Mu) = 0 P(Mu,Lambda) = ( +1 t^0 +1 t^2 ) Weyl(Mu, Lambda) = 110 Rank = 10 For Mu ( 3 , 0 , 0 , 3 ) and Lambda ( 4 , 2 , 0 , 3 ) That's Mu ( 3 , 3 , 3 , 3 ) and Lambda ( 5 , 6 , 5 , 4 ) in Root notation. l(Lambda) = 4; l(Mu) = 1 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 15 Rank = 3 For Mu ( 4 , 0 , 1 , 2 ) and Lambda ( 4 , 2 , 0 , 3 ) That's Mu ( 4 , 4 , 4 , 3 ) and Lambda ( 5 , 6 , 5 , 4 ) in Root notation. l(Lambda) = 4; l(Mu) = 2 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 8 Rank = 3 For Mu ( 2 , 1 , 0 , 4 ) and Lambda ( 4 , 2 , 0 , 3 ) That's Mu ( 3 , 4 , 4 , 4 ) and Lambda ( 5 , 6 , 5 , 4 ) in Root notation. l(Lambda) = 4; l(Mu) = 2 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 4 Rank = 1 For Mu ( 5 , 1 , 0 , 2 ) and Lambda ( 4 , 2 , 0 , 3 ) That's Mu ( 5 , 5 , 4 , 3 ) and Lambda ( 5 , 6 , 5 , 4 ) in Root notation. l(Lambda) = 4; l(Mu) = 3 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 3 Rank = 2 For Mu ( 3 , 1 , 1 , 3 ) and Lambda ( 4 , 2 , 0 , 3 ) That's Mu ( 4 , 5 , 5 , 4 ) and Lambda ( 5 , 6 , 5 , 4 ) in Root notation. l(Lambda) = 4; l(Mu) = 3 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 2 Rank = 1 For Mu ( 4 , 2 , 0 , 3 ) and Lambda ( 4 , 2 , 0 , 3 ) That's Mu ( 5 , 6 , 5 , 4 ) and Lambda ( 5 , 6 , 5 , 4 ) in Root notation. l(Lambda) = 4; l(Mu) = 4 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 1 Rank = 1 For Mu ( 0 , 0 , 0 , 0 ) and Lambda ( 3 , 0 , 2 , 4 ) That's Mu ( 0 , 0 , 0 , 0 ) and Lambda ( 4 , 5 , 6 , 5 ) in Root notation. l(Lambda) = 4; l(Mu) = 0 P(Mu,Lambda) = ( +1 t^0 +1 t^2 ) Weyl(Mu, Lambda) = 110 Rank = 10 For Mu ( 3 , 0 , 0 , 3 ) and Lambda ( 3 , 0 , 2 , 4 ) That's Mu ( 3 , 3 , 3 , 3 ) and Lambda ( 4 , 5 , 6 , 5 ) in Root notation. l(Lambda) = 4; l(Mu) = 1 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 15 Rank = 3 For Mu ( 4 , 0 , 1 , 2 ) and Lambda ( 3 , 0 , 2 , 4 ) That's Mu ( 4 , 4 , 4 , 3 ) and Lambda ( 4 , 5 , 6 , 5 ) in Root notation. l(Lambda) = 4; l(Mu) = 2 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 4 Rank = 1 For Mu ( 2 , 1 , 0 , 4 ) and Lambda ( 3 , 0 , 2 , 4 ) That's Mu ( 3 , 4 , 4 , 4 ) and Lambda ( 4 , 5 , 6 , 5 ) in Root notation. l(Lambda) = 4; l(Mu) = 2 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 8 Rank = 3 For Mu ( 3 , 1 , 1 , 3 ) and Lambda ( 3 , 0 , 2 , 4 ) That's Mu ( 4 , 5 , 5 , 4 ) and Lambda ( 4 , 5 , 6 , 5 ) in Root notation. l(Lambda) = 4; l(Mu) = 3 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 2 Rank = 1 For Mu ( 2 , 0 , 1 , 5 ) and Lambda ( 3 , 0 , 2 , 4 ) That's Mu ( 3 , 4 , 5 , 5 ) and Lambda ( 4 , 5 , 6 , 5 ) in Root notation. l(Lambda) = 4; l(Mu) = 3 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 3 Rank = 2 For Mu ( 3 , 0 , 2 , 4 ) and Lambda ( 3 , 0 , 2 , 4 ) That's Mu ( 4 , 5 , 6 , 5 ) and Lambda ( 4 , 5 , 6 , 5 ) in Root notation. l(Lambda) = 4; l(Mu) = 4 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 1 Rank = 1 For Mu ( 0 , 0 , 0 , 0 ) and Lambda ( 0 , 4 , 4 , 0 ) That's Mu ( 0 , 0 , 0 , 0 ) and Lambda ( 4 , 8 , 8 , 4 ) in Root notation. l(Lambda) = 4; l(Mu) = 0 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 85 Rank = 20 For Mu ( 3 , 0 , 0 , 3 ) and Lambda ( 0 , 4 , 4 , 0 ) That's Mu ( 3 , 3 , 3 , 3 ) and Lambda ( 4 , 8 , 8 , 4 ) in Root notation. l(Lambda) = 4; l(Mu) = 1 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 20 Rank = 11 For Mu ( 4 , 0 , 1 , 2 ) and Lambda ( 0 , 4 , 4 , 0 ) That's Mu ( 4 , 4 , 4 , 3 ) and Lambda ( 4 , 8 , 8 , 4 ) in Root notation. l(Lambda) = 4; l(Mu) = 2 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 8 Rank = 5 For Mu ( 2 , 1 , 0 , 4 ) and Lambda ( 0 , 4 , 4 , 0 ) That's Mu ( 3 , 4 , 4 , 4 ) and Lambda ( 4 , 8 , 8 , 4 ) in Root notation. l(Lambda) = 4; l(Mu) = 2 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 8 Rank = 5 For Mu ( 3 , 1 , 1 , 3 ) and Lambda ( 0 , 4 , 4 , 0 ) That's Mu ( 4 , 5 , 5 , 4 ) and Lambda ( 4 , 8 , 8 , 4 ) in Root notation. l(Lambda) = 4; l(Mu) = 3 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 4 Rank = 3 For Mu ( 0 , 4 , 4 , 0 ) and Lambda ( 0 , 4 , 4 , 0 ) That's Mu ( 4 , 8 , 8 , 4 ) and Lambda ( 4 , 8 , 8 , 4 ) in Root notation. l(Lambda) = 4; l(Mu) = 4 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 1 Rank = 1 For Mu ( 0 , 0 , 0 , 0 ) and Lambda ( 5 , 2 , 0 , 4 ) That's Mu ( 0 , 0 , 0 , 0 ) and Lambda ( 6 , 7 , 6 , 5 ) in Root notation. l(Lambda) = 5; l(Mu) = 0 P(Mu,Lambda) = ( +1 t^0 +2 t^2 +1 t^4 ) Weyl(Mu, Lambda) = 195 Rank = 74 For Mu ( 3 , 0 , 0 , 3 ) and Lambda ( 5 , 2 , 0 , 4 ) That's Mu ( 3 , 3 , 3 , 3 ) and Lambda ( 6 , 7 , 6 , 5 ) in Root notation. l(Lambda) = 5; l(Mu) = 1 P(Mu,Lambda) = ( +1 t^0 +1 t^2 ) Weyl(Mu, Lambda) = 42 Rank = 24 For Mu ( 4 , 0 , 1 , 2 ) and Lambda ( 5 , 2 , 0 , 4 ) That's Mu ( 4 , 4 , 4 , 3 ) and Lambda ( 6 , 7 , 6 , 5 ) in Root notation. l(Lambda) = 5; l(Mu) = 2 P(Mu,Lambda) = ( +1 t^0 +1 t^2 ) Weyl(Mu, Lambda) = 27 Rank = 18 For Mu ( 2 , 1 , 0 , 4 ) and Lambda ( 5 , 2 , 0 , 4 ) That's Mu ( 3 , 4 , 4 , 4 ) and Lambda ( 6 , 7 , 6 , 5 ) in Root notation. l(Lambda) = 5; l(Mu) = 2 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 18 Rank = 11 For Mu ( 5 , 1 , 0 , 2 ) and Lambda ( 5 , 2 , 0 , 4 ) That's Mu ( 5 , 5 , 4 , 3 ) and Lambda ( 6 , 7 , 6 , 5 ) in Root notation. l(Lambda) = 5; l(Mu) = 3 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 15 Rank = 12 For Mu ( 3 , 1 , 1 , 3 ) and Lambda ( 5 , 2 , 0 , 4 ) That's Mu ( 4 , 5 , 5 , 4 ) and Lambda ( 6 , 7 , 6 , 5 ) in Root notation. l(Lambda) = 5; l(Mu) = 3 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 11 Rank = 8 For Mu ( 2 , 0 , 1 , 5 ) and Lambda ( 5 , 2 , 0 , 4 ) That's Mu ( 3 , 4 , 5 , 5 ) and Lambda ( 6 , 7 , 6 , 5 ) in Root notation. l(Lambda) = 5; l(Mu) = 3 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 5 Rank = 3 For Mu ( 4 , 2 , 0 , 3 ) and Lambda ( 5 , 2 , 0 , 4 ) That's Mu ( 5 , 6 , 5 , 4 ) and Lambda ( 6 , 7 , 6 , 5 ) in Root notation. l(Lambda) = 5; l(Mu) = 4 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 6 Rank = 5 For Mu ( 3 , 0 , 2 , 4 ) and Lambda ( 5 , 2 , 0 , 4 ) That's Mu ( 4 , 5 , 6 , 5 ) and Lambda ( 6 , 7 , 6 , 5 ) in Root notation. l(Lambda) = 5; l(Mu) = 4 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 3 Rank = 2 For Mu ( 5 , 2 , 0 , 4 ) and Lambda ( 5 , 2 , 0 , 4 ) That's Mu ( 6 , 7 , 6 , 5 ) and Lambda ( 6 , 7 , 6 , 5 ) in Root notation. l(Lambda) = 5; l(Mu) = 5 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 1 Rank = 1 For Mu ( 7 , 0 , 0 , 2 ) and Lambda ( 5 , 2 , 0 , 4 ) That's Mu ( 6 , 5 , 4 , 3 ) and Lambda ( 6 , 7 , 6 , 5 ) in Root notation. l(Lambda) = 5; l(Mu) = 4 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 6 Rank = 5 For Mu ( 0 , 0 , 0 , 0 ) and Lambda ( 1 , 5 , 3 , 0 ) That's Mu ( 0 , 0 , 0 , 0 ) and Lambda ( 5 , 9 , 8 , 4 ) in Root notation. l(Lambda) = 5; l(Mu) = 0 P(Mu,Lambda) = ( +1 t^0 +1 t^2 ) Weyl(Mu, Lambda) = 160 Rank = 40 For Mu ( 3 , 0 , 0 , 3 ) and Lambda ( 1 , 5 , 3 , 0 ) That's Mu ( 3 , 3 , 3 , 3 ) and Lambda ( 5 , 9 , 8 , 4 ) in Root notation. l(Lambda) = 5; l(Mu) = 1 P(Mu,Lambda) = ( +1 t^0 +1 t^2 ) Weyl(Mu, Lambda) = 44 Rank = 19 For Mu ( 4 , 0 , 1 , 2 ) and Lambda ( 1 , 5 , 3 , 0 ) That's Mu ( 4 , 4 , 4 , 3 ) and Lambda ( 5 , 9 , 8 , 4 ) in Root notation. l(Lambda) = 5; l(Mu) = 2 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 24 Rank = 13 For Mu ( 2 , 1 , 0 , 4 ) and Lambda ( 1 , 5 , 3 , 0 ) That's Mu ( 3 , 4 , 4 , 4 ) and Lambda ( 5 , 9 , 8 , 4 ) in Root notation. l(Lambda) = 5; l(Mu) = 2 P(Mu,Lambda) = ( +1 t^0 +1 t^2 ) Weyl(Mu, Lambda) = 18 Rank = 8 For Mu ( 5 , 1 , 0 , 2 ) and Lambda ( 1 , 5 , 3 , 0 ) That's Mu ( 5 , 5 , 4 , 3 ) and Lambda ( 5 , 9 , 8 , 4 ) in Root notation. l(Lambda) = 5; l(Mu) = 3 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 7 Rank = 5 For Mu ( 3 , 1 , 1 , 3 ) and Lambda ( 1 , 5 , 3 , 0 ) That's Mu ( 4 , 5 , 5 , 4 ) and Lambda ( 5 , 9 , 8 , 4 ) in Root notation. l(Lambda) = 5; l(Mu) = 3 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 11 Rank = 6 For Mu ( 4 , 2 , 0 , 3 ) and Lambda ( 1 , 5 , 3 , 0 ) That's Mu ( 5 , 6 , 5 , 4 ) and Lambda ( 5 , 9 , 8 , 4 ) in Root notation. l(Lambda) = 5; l(Mu) = 4 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 4 Rank = 3 For Mu ( 0 , 4 , 4 , 0 ) and Lambda ( 1 , 5 , 3 , 0 ) That's Mu ( 4 , 8 , 8 , 4 ) and Lambda ( 5 , 9 , 8 , 4 ) in Root notation. l(Lambda) = 5; l(Mu) = 4 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 2 Rank = 1 For Mu ( 1 , 5 , 3 , 0 ) and Lambda ( 1 , 5 , 3 , 0 ) That's Mu ( 5 , 9 , 8 , 4 ) and Lambda ( 5 , 9 , 8 , 4 ) in Root notation. l(Lambda) = 5; l(Mu) = 5 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 1 Rank = 1 For Mu ( 0 , 0 , 0 , 0 ) and Lambda ( 4 , 0 , 2 , 5 ) That's Mu ( 0 , 0 , 0 , 0 ) and Lambda ( 5 , 6 , 7 , 6 ) in Root notation. l(Lambda) = 5; l(Mu) = 0 P(Mu,Lambda) = ( +1 t^0 +2 t^2 +1 t^4 ) Weyl(Mu, Lambda) = 195 Rank = 74 For Mu ( 3 , 0 , 0 , 3 ) and Lambda ( 4 , 0 , 2 , 5 ) That's Mu ( 3 , 3 , 3 , 3 ) and Lambda ( 5 , 6 , 7 , 6 ) in Root notation. l(Lambda) = 5; l(Mu) = 1 P(Mu,Lambda) = ( +1 t^0 +1 t^2 ) Weyl(Mu, Lambda) = 42 Rank = 24 For Mu ( 4 , 0 , 1 , 2 ) and Lambda ( 4 , 0 , 2 , 5 ) That's Mu ( 4 , 4 , 4 , 3 ) and Lambda ( 5 , 6 , 7 , 6 ) in Root notation. l(Lambda) = 5; l(Mu) = 2 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 18 Rank = 11 For Mu ( 2 , 1 , 0 , 4 ) and Lambda ( 4 , 0 , 2 , 5 ) That's Mu ( 3 , 4 , 4 , 4 ) and Lambda ( 5 , 6 , 7 , 6 ) in Root notation. l(Lambda) = 5; l(Mu) = 2 P(Mu,Lambda) = ( +1 t^0 +1 t^2 ) Weyl(Mu, Lambda) = 27 Rank = 18 For Mu ( 5 , 1 , 0 , 2 ) and Lambda ( 4 , 0 , 2 , 5 ) That's Mu ( 5 , 5 , 4 , 3 ) and Lambda ( 5 , 6 , 7 , 6 ) in Root notation. l(Lambda) = 5; l(Mu) = 3 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 5 Rank = 3 For Mu ( 3 , 1 , 1 , 3 ) and Lambda ( 4 , 0 , 2 , 5 ) That's Mu ( 4 , 5 , 5 , 4 ) and Lambda ( 5 , 6 , 7 , 6 ) in Root notation. l(Lambda) = 5; l(Mu) = 3 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 11 Rank = 8 For Mu ( 2 , 0 , 1 , 5 ) and Lambda ( 4 , 0 , 2 , 5 ) That's Mu ( 3 , 4 , 5 , 5 ) and Lambda ( 5 , 6 , 7 , 6 ) in Root notation. l(Lambda) = 5; l(Mu) = 3 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 15 Rank = 12 For Mu ( 4 , 2 , 0 , 3 ) and Lambda ( 4 , 0 , 2 , 5 ) That's Mu ( 5 , 6 , 5 , 4 ) and Lambda ( 5 , 6 , 7 , 6 ) in Root notation. l(Lambda) = 5; l(Mu) = 4 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 3 Rank = 2 For Mu ( 3 , 0 , 2 , 4 ) and Lambda ( 4 , 0 , 2 , 5 ) That's Mu ( 4 , 5 , 6 , 5 ) and Lambda ( 5 , 6 , 7 , 6 ) in Root notation. l(Lambda) = 5; l(Mu) = 4 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 6 Rank = 5 For Mu ( 4 , 0 , 2 , 5 ) and Lambda ( 4 , 0 , 2 , 5 ) That's Mu ( 5 , 6 , 7 , 6 ) and Lambda ( 5 , 6 , 7 , 6 ) in Root notation. l(Lambda) = 5; l(Mu) = 5 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 1 Rank = 1 For Mu ( 2 , 0 , 0 , 7 ) and Lambda ( 4 , 0 , 2 , 5 ) That's Mu ( 3 , 4 , 5 , 6 ) and Lambda ( 5 , 6 , 7 , 6 ) in Root notation. l(Lambda) = 5; l(Mu) = 4 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 6 Rank = 5 For Mu ( 0 , 0 , 0 , 0 ) and Lambda ( 0 , 3 , 5 , 1 ) That's Mu ( 0 , 0 , 0 , 0 ) and Lambda ( 4 , 8 , 9 , 5 ) in Root notation. l(Lambda) = 5; l(Mu) = 0 P(Mu,Lambda) = ( +1 t^0 +1 t^2 ) Weyl(Mu, Lambda) = 160 Rank = 40 For Mu ( 3 , 0 , 0 , 3 ) and Lambda ( 0 , 3 , 5 , 1 ) That's Mu ( 3 , 3 , 3 , 3 ) and Lambda ( 4 , 8 , 9 , 5 ) in Root notation. l(Lambda) = 5; l(Mu) = 1 P(Mu,Lambda) = ( +1 t^0 +1 t^2 ) Weyl(Mu, Lambda) = 44 Rank = 19 For Mu ( 4 , 0 , 1 , 2 ) and Lambda ( 0 , 3 , 5 , 1 ) That's Mu ( 4 , 4 , 4 , 3 ) and Lambda ( 4 , 8 , 9 , 5 ) in Root notation. l(Lambda) = 5; l(Mu) = 2 P(Mu,Lambda) = ( +1 t^0 +1 t^2 ) Weyl(Mu, Lambda) = 18 Rank = 8 For Mu ( 2 , 1 , 0 , 4 ) and Lambda ( 0 , 3 , 5 , 1 ) That's Mu ( 3 , 4 , 4 , 4 ) and Lambda ( 4 , 8 , 9 , 5 ) in Root notation. l(Lambda) = 5; l(Mu) = 2 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 24 Rank = 13 For Mu ( 3 , 1 , 1 , 3 ) and Lambda ( 0 , 3 , 5 , 1 ) That's Mu ( 4 , 5 , 5 , 4 ) and Lambda ( 4 , 8 , 9 , 5 ) in Root notation. l(Lambda) = 5; l(Mu) = 3 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 11 Rank = 6 For Mu ( 2 , 0 , 1 , 5 ) and Lambda ( 0 , 3 , 5 , 1 ) That's Mu ( 3 , 4 , 5 , 5 ) and Lambda ( 4 , 8 , 9 , 5 ) in Root notation. l(Lambda) = 5; l(Mu) = 3 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 7 Rank = 5 For Mu ( 3 , 0 , 2 , 4 ) and Lambda ( 0 , 3 , 5 , 1 ) That's Mu ( 4 , 5 , 6 , 5 ) and Lambda ( 4 , 8 , 9 , 5 ) in Root notation. l(Lambda) = 5; l(Mu) = 4 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 4 Rank = 3 For Mu ( 0 , 4 , 4 , 0 ) and Lambda ( 0 , 3 , 5 , 1 ) That's Mu ( 4 , 8 , 8 , 4 ) and Lambda ( 4 , 8 , 9 , 5 ) in Root notation. l(Lambda) = 5; l(Mu) = 4 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 2 Rank = 1 For Mu ( 0 , 3 , 5 , 1 ) and Lambda ( 0 , 3 , 5 , 1 ) That's Mu ( 4 , 8 , 9 , 5 ) and Lambda ( 4 , 8 , 9 , 5 ) in Root notation. l(Lambda) = 5; l(Mu) = 5 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 1 Rank = 1 For Mu ( 0 , 0 , 0 , 0 ) and Lambda ( 5 , 1 , 1 , 5 ) That's Mu ( 0 , 0 , 0 , 0 ) and Lambda ( 6 , 7 , 7 , 6 ) in Root notation. l(Lambda) = 6; l(Mu) = 0 P(Mu,Lambda) = ( +1 t^0 +1 t^2 +2 t^4 ) Weyl(Mu, Lambda) = 400 Rank = 96 For Mu ( 3 , 0 , 0 , 3 ) and Lambda ( 5 , 1 , 1 , 5 ) That's Mu ( 3 , 3 , 3 , 3 ) and Lambda ( 6 , 7 , 7 , 6 ) in Root notation. l(Lambda) = 6; l(Mu) = 1 P(Mu,Lambda) = ( +1 t^0 +1 t^4 ) Weyl(Mu, Lambda) = 100 Rank = 32 For Mu ( 4 , 0 , 1 , 2 ) and Lambda ( 5 , 1 , 1 , 5 ) That's Mu ( 4 , 4 , 4 , 3 ) and Lambda ( 6 , 7 , 7 , 6 ) in Root notation. l(Lambda) = 6; l(Mu) = 2 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 56 Rank = 19 For Mu ( 2 , 1 , 0 , 4 ) and Lambda ( 5 , 1 , 1 , 5 ) That's Mu ( 3 , 4 , 4 , 4 ) and Lambda ( 6 , 7 , 7 , 6 ) in Root notation. l(Lambda) = 6; l(Mu) = 2 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 56 Rank = 19 For Mu ( 5 , 1 , 0 , 2 ) and Lambda ( 5 , 1 , 1 , 5 ) That's Mu ( 5 , 5 , 4 , 3 ) and Lambda ( 6 , 7 , 7 , 6 ) in Root notation. l(Lambda) = 6; l(Mu) = 3 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 26 Rank = 9 For Mu ( 3 , 1 , 1 , 3 ) and Lambda ( 5 , 1 , 1 , 5 ) That's Mu ( 4 , 5 , 5 , 4 ) and Lambda ( 6 , 7 , 7 , 6 ) in Root notation. l(Lambda) = 6; l(Mu) = 3 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 29 Rank = 10 For Mu ( 2 , 0 , 1 , 5 ) and Lambda ( 5 , 1 , 1 , 5 ) That's Mu ( 3 , 4 , 5 , 5 ) and Lambda ( 6 , 7 , 7 , 6 ) in Root notation. l(Lambda) = 6; l(Mu) = 3 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 26 Rank = 9 For Mu ( 4 , 2 , 0 , 3 ) and Lambda ( 5 , 1 , 1 , 5 ) That's Mu ( 5 , 6 , 5 , 4 ) and Lambda ( 6 , 7 , 7 , 6 ) in Root notation. l(Lambda) = 6; l(Mu) = 4 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 12 Rank = 4 For Mu ( 3 , 0 , 2 , 4 ) and Lambda ( 5 , 1 , 1 , 5 ) That's Mu ( 4 , 5 , 6 , 5 ) and Lambda ( 6 , 7 , 7 , 6 ) in Root notation. l(Lambda) = 6; l(Mu) = 4 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 12 Rank = 4 For Mu ( 5 , 2 , 0 , 4 ) and Lambda ( 5 , 1 , 1 , 5 ) That's Mu ( 6 , 7 , 6 , 5 ) and Lambda ( 6 , 7 , 7 , 6 ) in Root notation. l(Lambda) = 6; l(Mu) = 5 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 2 Rank = 1 For Mu ( 4 , 0 , 2 , 5 ) and Lambda ( 5 , 1 , 1 , 5 ) That's Mu ( 5 , 6 , 7 , 6 ) and Lambda ( 6 , 7 , 7 , 6 ) in Root notation. l(Lambda) = 6; l(Mu) = 5 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 2 Rank = 1 For Mu ( 5 , 1 , 1 , 5 ) and Lambda ( 5 , 1 , 1 , 5 ) That's Mu ( 6 , 7 , 7 , 6 ) and Lambda ( 6 , 7 , 7 , 6 ) in Root notation. l(Lambda) = 6; l(Mu) = 6 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 1 Rank = 1 For Mu ( 7 , 0 , 0 , 2 ) and Lambda ( 5 , 1 , 1 , 5 ) That's Mu ( 6 , 5 , 4 , 3 ) and Lambda ( 6 , 7 , 7 , 6 ) in Root notation. l(Lambda) = 6; l(Mu) = 4 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 8 Rank = 3 For Mu ( 2 , 0 , 0 , 7 ) and Lambda ( 5 , 1 , 1 , 5 ) That's Mu ( 3 , 4 , 5 , 6 ) and Lambda ( 6 , 7 , 7 , 6 ) in Root notation. l(Lambda) = 6; l(Mu) = 4 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 8 Rank = 3 For Mu ( 0 , 0 , 0 , 0 ) and Lambda ( 2 , 5 , 3 , 1 ) That's Mu ( 0 , 0 , 0 , 0 ) and Lambda ( 6 , 10 , 9 , 5 ) in Root notation. l(Lambda) = 6; l(Mu) = 0 P(Mu,Lambda) = ( +1 t^0 +2 t^2 +1 t^4 ) Weyl(Mu, Lambda) = 600 Rank = 260 For Mu ( 3 , 0 , 0 , 3 ) and Lambda ( 2 , 5 , 3 , 1 ) That's Mu ( 3 , 3 , 3 , 3 ) and Lambda ( 6 , 10 , 9 , 5 ) in Root notation. l(Lambda) = 6; l(Mu) = 1 P(Mu,Lambda) = ( +1 t^0 +2 t^2 +1 t^4 ) Weyl(Mu, Lambda) = 210 Rank = 116 For Mu ( 4 , 0 , 1 , 2 ) and Lambda ( 2 , 5 , 3 , 1 ) That's Mu ( 4 , 4 , 4 , 3 ) and Lambda ( 6 , 10 , 9 , 5 ) in Root notation. l(Lambda) = 6; l(Mu) = 2 P(Mu,Lambda) = ( +1 t^0 +1 t^2 ) Weyl(Mu, Lambda) = 132 Rank = 80 For Mu ( 2 , 1 , 0 , 4 ) and Lambda ( 2 , 5 , 3 , 1 ) That's Mu ( 3 , 4 , 4 , 4 ) and Lambda ( 6 , 10 , 9 , 5 ) in Root notation. l(Lambda) = 6; l(Mu) = 2 P(Mu,Lambda) = ( +1 t^0 +1 t^2 ) Weyl(Mu, Lambda) = 110 Rank = 64 For Mu ( 5 , 1 , 0 , 2 ) and Lambda ( 2 , 5 , 3 , 1 ) That's Mu ( 5 , 5 , 4 , 3 ) and Lambda ( 6 , 10 , 9 , 5 ) in Root notation. l(Lambda) = 6; l(Mu) = 3 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 62 Rank = 43 For Mu ( 3 , 1 , 1 , 3 ) and Lambda ( 2 , 5 , 3 , 1 ) That's Mu ( 4 , 5 , 5 , 4 ) and Lambda ( 6 , 10 , 9 , 5 ) in Root notation. l(Lambda) = 6; l(Mu) = 3 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 72 Rank = 46 For Mu ( 2 , 0 , 1 , 5 ) and Lambda ( 2 , 5 , 3 , 1 ) That's Mu ( 3 , 4 , 5 , 5 ) and Lambda ( 6 , 10 , 9 , 5 ) in Root notation. l(Lambda) = 6; l(Mu) = 3 P(Mu,Lambda) = ( +1 t^0 +1 t^2 ) Weyl(Mu, Lambda) = 30 Rank = 19 For Mu ( 4 , 2 , 0 , 3 ) and Lambda ( 2 , 5 , 3 , 1 ) That's Mu ( 5 , 6 , 5 , 4 ) and Lambda ( 6 , 10 , 9 , 5 ) in Root notation. l(Lambda) = 6; l(Mu) = 4 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 36 Rank = 27 For Mu ( 3 , 0 , 2 , 4 ) and Lambda ( 2 , 5 , 3 , 1 ) That's Mu ( 4 , 5 , 6 , 5 ) and Lambda ( 6 , 10 , 9 , 5 ) in Root notation. l(Lambda) = 6; l(Mu) = 4 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 20 Rank = 14 For Mu ( 0 , 4 , 4 , 0 ) and Lambda ( 2 , 5 , 3 , 1 ) That's Mu ( 4 , 8 , 8 , 4 ) and Lambda ( 6 , 10 , 9 , 5 ) in Root notation. l(Lambda) = 6; l(Mu) = 4 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 14 Rank = 11 For Mu ( 5 , 2 , 0 , 4 ) and Lambda ( 2 , 5 , 3 , 1 ) That's Mu ( 6 , 7 , 6 , 5 ) and Lambda ( 6 , 10 , 9 , 5 ) in Root notation. l(Lambda) = 6; l(Mu) = 5 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 4 Rank = 3 For Mu ( 1 , 5 , 3 , 0 ) and Lambda ( 2 , 5 , 3 , 1 ) That's Mu ( 5 , 9 , 8 , 4 ) and Lambda ( 6 , 10 , 9 , 5 ) in Root notation. l(Lambda) = 6; l(Mu) = 5 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 8 Rank = 7 For Mu ( 0 , 3 , 5 , 1 ) and Lambda ( 2 , 5 , 3 , 1 ) That's Mu ( 4 , 8 , 9 , 5 ) and Lambda ( 6 , 10 , 9 , 5 ) in Root notation. l(Lambda) = 6; l(Mu) = 5 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 3 Rank = 2 For Mu ( 2 , 5 , 3 , 1 ) and Lambda ( 2 , 5 , 3 , 1 ) That's Mu ( 6 , 10 , 9 , 5 ) and Lambda ( 6 , 10 , 9 , 5 ) in Root notation. l(Lambda) = 6; l(Mu) = 6 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 1 Rank = 1 For Mu ( 7 , 0 , 0 , 2 ) and Lambda ( 2 , 5 , 3 , 1 ) That's Mu ( 6 , 5 , 4 , 3 ) and Lambda ( 6 , 10 , 9 , 5 ) in Root notation. l(Lambda) = 6; l(Mu) = 4 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 18 Rank = 13 For Mu ( 0 , 7 , 2 , 0 ) and Lambda ( 2 , 5 , 3 , 1 ) That's Mu ( 5 , 10 , 8 , 4 ) and Lambda ( 6 , 10 , 9 , 5 ) in Root notation. l(Lambda) = 6; l(Mu) = 6 P(Mu,Lambda) = ( ) Weyl(Mu, Lambda) = 2 Rank = 2 For Mu ( 0 , 0 , 0 , 0 ) and Lambda ( 1 , 3 , 5 , 2 ) That's Mu ( 0 , 0 , 0 , 0 ) and Lambda ( 5 , 9 , 10 , 6 ) in Root notation. l(Lambda) = 6; l(Mu) = 0 P(Mu,Lambda) = ( +1 t^0 +2 t^2 +1 t^4 ) Weyl(Mu, Lambda) = 600 Rank = 260 For Mu ( 3 , 0 , 0 , 3 ) and Lambda ( 1 , 3 , 5 , 2 ) That's Mu ( 3 , 3 , 3 , 3 ) and Lambda ( 5 , 9 , 10 , 6 ) in Root notation. l(Lambda) = 6; l(Mu) = 1 P(Mu,Lambda) = ( +1 t^0 +2 t^2 +1 t^4 ) Weyl(Mu, Lambda) = 210 Rank = 116 For Mu ( 4 , 0 , 1 , 2 ) and Lambda ( 1 , 3 , 5 , 2 ) That's Mu ( 4 , 4 , 4 , 3 ) and Lambda ( 5 , 9 , 10 , 6 ) in Root notation. l(Lambda) = 6; l(Mu) = 2 P(Mu,Lambda) = ( +1 t^0 +1 t^2 ) Weyl(Mu, Lambda) = 110 Rank = 64 For Mu ( 2 , 1 , 0 , 4 ) and Lambda ( 1 , 3 , 5 , 2 ) That's Mu ( 3 , 4 , 4 , 4 ) and Lambda ( 5 , 9 , 10 , 6 ) in Root notation. l(Lambda) = 6; l(Mu) = 2 P(Mu,Lambda) = ( +1 t^0 +1 t^2 ) Weyl(Mu, Lambda) = 132 Rank = 80 For Mu ( 5 , 1 , 0 , 2 ) and Lambda ( 1 , 3 , 5 , 2 ) That's Mu ( 5 , 5 , 4 , 3 ) and Lambda ( 5 , 9 , 10 , 6 ) in Root notation. l(Lambda) = 6; l(Mu) = 3 P(Mu,Lambda) = ( +1 t^0 +1 t^2 ) Weyl(Mu, Lambda) = 30 Rank = 19 For Mu ( 3 , 1 , 1 , 3 ) and Lambda ( 1 , 3 , 5 , 2 ) That's Mu ( 4 , 5 , 5 , 4 ) and Lambda ( 5 , 9 , 10 , 6 ) in Root notation. l(Lambda) = 6; l(Mu) = 3 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 72 Rank = 46 For Mu ( 2 , 0 , 1 , 5 ) and Lambda ( 1 , 3 , 5 , 2 ) That's Mu ( 3 , 4 , 5 , 5 ) and Lambda ( 5 , 9 , 10 , 6 ) in Root notation. l(Lambda) = 6; l(Mu) = 3 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 62 Rank = 43 For Mu ( 4 , 2 , 0 , 3 ) and Lambda ( 1 , 3 , 5 , 2 ) That's Mu ( 5 , 6 , 5 , 4 ) and Lambda ( 5 , 9 , 10 , 6 ) in Root notation. l(Lambda) = 6; l(Mu) = 4 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 20 Rank = 14 For Mu ( 3 , 0 , 2 , 4 ) and Lambda ( 1 , 3 , 5 , 2 ) That's Mu ( 4 , 5 , 6 , 5 ) and Lambda ( 5 , 9 , 10 , 6 ) in Root notation. l(Lambda) = 6; l(Mu) = 4 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 36 Rank = 27 For Mu ( 0 , 4 , 4 , 0 ) and Lambda ( 1 , 3 , 5 , 2 ) That's Mu ( 4 , 8 , 8 , 4 ) and Lambda ( 5 , 9 , 10 , 6 ) in Root notation. l(Lambda) = 6; l(Mu) = 4 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 14 Rank = 11 For Mu ( 1 , 5 , 3 , 0 ) and Lambda ( 1 , 3 , 5 , 2 ) That's Mu ( 5 , 9 , 8 , 4 ) and Lambda ( 5 , 9 , 10 , 6 ) in Root notation. l(Lambda) = 6; l(Mu) = 5 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 3 Rank = 2 For Mu ( 4 , 0 , 2 , 5 ) and Lambda ( 1 , 3 , 5 , 2 ) That's Mu ( 5 , 6 , 7 , 6 ) and Lambda ( 5 , 9 , 10 , 6 ) in Root notation. l(Lambda) = 6; l(Mu) = 5 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 4 Rank = 3 For Mu ( 0 , 3 , 5 , 1 ) and Lambda ( 1 , 3 , 5 , 2 ) That's Mu ( 4 , 8 , 9 , 5 ) and Lambda ( 5 , 9 , 10 , 6 ) in Root notation. l(Lambda) = 6; l(Mu) = 5 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 8 Rank = 7 For Mu ( 1 , 3 , 5 , 2 ) and Lambda ( 1 , 3 , 5 , 2 ) That's Mu ( 5 , 9 , 10 , 6 ) and Lambda ( 5 , 9 , 10 , 6 ) in Root notation. l(Lambda) = 6; l(Mu) = 6 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 1 Rank = 1 For Mu ( 2 , 0 , 0 , 7 ) and Lambda ( 1 , 3 , 5 , 2 ) That's Mu ( 3 , 4 , 5 , 6 ) and Lambda ( 5 , 9 , 10 , 6 ) in Root notation. l(Lambda) = 6; l(Mu) = 4 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 18 Rank = 13 For Mu ( 0 , 2 , 7 , 0 ) and Lambda ( 1 , 3 , 5 , 2 ) That's Mu ( 4 , 8 , 10 , 5 ) and Lambda ( 5 , 9 , 10 , 6 ) in Root notation. l(Lambda) = 6; l(Mu) = 6 P(Mu,Lambda) = ( ) Weyl(Mu, Lambda) = 2 Rank = 2 For Mu ( 0 , 0 , 0 , 0 ) and Lambda ( 2 , 4 , 4 , 2 ) That's Mu ( 0 , 0 , 0 , 0 ) and Lambda ( 6 , 10 , 10 , 6 ) in Root notation. l(Lambda) = 7; l(Mu) = 0 P(Mu,Lambda) = ( +1 t^0 +2 t^2 +2 t^4 ) Weyl(Mu, Lambda) = 1130 Rank = 90 For Mu ( 3 , 0 , 0 , 3 ) and Lambda ( 2 , 4 , 4 , 2 ) That's Mu ( 3 , 3 , 3 , 3 ) and Lambda ( 6 , 10 , 10 , 6 ) in Root notation. l(Lambda) = 7; l(Mu) = 1 P(Mu,Lambda) = ( +1 t^0 +2 t^2 +2 t^4 ) Weyl(Mu, Lambda) = 428 Rank = 45 For Mu ( 4 , 0 , 1 , 2 ) and Lambda ( 2 , 4 , 4 , 2 ) That's Mu ( 4 , 4 , 4 , 3 ) and Lambda ( 6 , 10 , 10 , 6 ) in Root notation. l(Lambda) = 7; l(Mu) = 2 P(Mu,Lambda) = ( +1 t^0 +1 t^2 ) Weyl(Mu, Lambda) = 261 Rank = 34 For Mu ( 2 , 1 , 0 , 4 ) and Lambda ( 2 , 4 , 4 , 2 ) That's Mu ( 3 , 4 , 4 , 4 ) and Lambda ( 6 , 10 , 10 , 6 ) in Root notation. l(Lambda) = 7; l(Mu) = 2 P(Mu,Lambda) = ( +1 t^0 +1 t^2 ) Weyl(Mu, Lambda) = 261 Rank = 34 For Mu ( 5 , 1 , 0 , 2 ) and Lambda ( 2 , 4 , 4 , 2 ) That's Mu ( 5 , 5 , 4 , 3 ) and Lambda ( 6 , 10 , 10 , 6 ) in Root notation. l(Lambda) = 7; l(Mu) = 3 P(Mu,Lambda) = ( +1 t^0 +1 t^2 ) Weyl(Mu, Lambda) = 117 Rank = 23 For Mu ( 3 , 1 , 1 , 3 ) and Lambda ( 2 , 4 , 4 , 2 ) That's Mu ( 4 , 5 , 5 , 4 ) and Lambda ( 6 , 10 , 10 , 6 ) in Root notation. l(Lambda) = 7; l(Mu) = 3 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 162 Rank = 26 For Mu ( 2 , 0 , 1 , 5 ) and Lambda ( 2 , 4 , 4 , 2 ) That's Mu ( 3 , 4 , 5 , 5 ) and Lambda ( 6 , 10 , 10 , 6 ) in Root notation. l(Lambda) = 7; l(Mu) = 3 P(Mu,Lambda) = ( +1 t^0 +1 t^2 ) Weyl(Mu, Lambda) = 117 Rank = 23 For Mu ( 4 , 2 , 0 , 3 ) and Lambda ( 2 , 4 , 4 , 2 ) That's Mu ( 5 , 6 , 5 , 4 ) and Lambda ( 6 , 10 , 10 , 6 ) in Root notation. l(Lambda) = 7; l(Mu) = 4 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 73 Rank = 17 For Mu ( 3 , 0 , 2 , 4 ) and Lambda ( 2 , 4 , 4 , 2 ) That's Mu ( 4 , 5 , 6 , 5 ) and Lambda ( 6 , 10 , 10 , 6 ) in Root notation. l(Lambda) = 7; l(Mu) = 4 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 73 Rank = 17 For Mu ( 0 , 4 , 4 , 0 ) and Lambda ( 2 , 4 , 4 , 2 ) That's Mu ( 4 , 8 , 8 , 4 ) and Lambda ( 6 , 10 , 10 , 6 ) in Root notation. l(Lambda) = 7; l(Mu) = 4 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 35 Rank = 10 For Mu ( 5 , 2 , 0 , 4 ) and Lambda ( 2 , 4 , 4 , 2 ) That's Mu ( 6 , 7 , 6 , 5 ) and Lambda ( 6 , 10 , 10 , 6 ) in Root notation. l(Lambda) = 7; l(Mu) = 5 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 11 Rank = 6 For Mu ( 1 , 5 , 3 , 0 ) and Lambda ( 2 , 4 , 4 , 2 ) That's Mu ( 5 , 9 , 8 , 4 ) and Lambda ( 6 , 10 , 10 , 6 ) in Root notation. l(Lambda) = 7; l(Mu) = 5 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 14 Rank = 4 For Mu ( 4 , 0 , 2 , 5 ) and Lambda ( 2 , 4 , 4 , 2 ) That's Mu ( 5 , 6 , 7 , 6 ) and Lambda ( 6 , 10 , 10 , 6 ) in Root notation. l(Lambda) = 7; l(Mu) = 5 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 11 Rank = 6 For Mu ( 0 , 3 , 5 , 1 ) and Lambda ( 2 , 4 , 4 , 2 ) That's Mu ( 4 , 8 , 9 , 5 ) and Lambda ( 6 , 10 , 10 , 6 ) in Root notation. l(Lambda) = 7; l(Mu) = 5 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 14 Rank = 4 For Mu ( 5 , 1 , 1 , 5 ) and Lambda ( 2 , 4 , 4 , 2 ) That's Mu ( 6 , 7 , 7 , 6 ) and Lambda ( 6 , 10 , 10 , 6 ) in Root notation. l(Lambda) = 7; l(Mu) = 6 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 4 Rank = 3 For Mu ( 2 , 5 , 3 , 1 ) and Lambda ( 2 , 4 , 4 , 2 ) That's Mu ( 6 , 10 , 9 , 5 ) and Lambda ( 6 , 10 , 10 , 6 ) in Root notation. l(Lambda) = 7; l(Mu) = 6 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 2 Rank = 1 For Mu ( 1 , 3 , 5 , 2 ) and Lambda ( 2 , 4 , 4 , 2 ) That's Mu ( 5 , 9 , 10 , 6 ) and Lambda ( 6 , 10 , 10 , 6 ) in Root notation. l(Lambda) = 7; l(Mu) = 6 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 2 Rank = 1 For Mu ( 2 , 4 , 4 , 2 ) and Lambda ( 2 , 4 , 4 , 2 ) That's Mu ( 6 , 10 , 10 , 6 ) and Lambda ( 6 , 10 , 10 , 6 ) in Root notation. l(Lambda) = 7; l(Mu) = 7 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 1 Rank = 1 For Mu ( 7 , 0 , 0 , 2 ) and Lambda ( 2 , 4 , 4 , 2 ) That's Mu ( 6 , 5 , 4 , 3 ) and Lambda ( 6 , 10 , 10 , 6 ) in Root notation. l(Lambda) = 7; l(Mu) = 4 P(Mu,Lambda) = ( +1 t^0 +1 t^2 ) Weyl(Mu, Lambda) = 33 Rank = 11 For Mu ( 2 , 0 , 0 , 7 ) and Lambda ( 2 , 4 , 4 , 2 ) That's Mu ( 3 , 4 , 5 , 6 ) and Lambda ( 6 , 10 , 10 , 6 ) in Root notation. l(Lambda) = 7; l(Mu) = 4 P(Mu,Lambda) = ( +1 t^0 +1 t^2 ) Weyl(Mu, Lambda) = 33 Rank = 11 For Mu ( 0 , 7 , 2 , 0 ) and Lambda ( 2 , 4 , 4 , 2 ) That's Mu ( 5 , 10 , 8 , 4 ) and Lambda ( 6 , 10 , 10 , 6 ) in Root notation. l(Lambda) = 7; l(Mu) = 6 P(Mu,Lambda) = ( ) Weyl(Mu, Lambda) = 3 Rank = 1 For Mu ( 0 , 2 , 7 , 0 ) and Lambda ( 2 , 4 , 4 , 2 ) That's Mu ( 4 , 8 , 10 , 5 ) and Lambda ( 6 , 10 , 10 , 6 ) in Root notation. l(Lambda) = 7; l(Mu) = 6 P(Mu,Lambda) = ( ) Weyl(Mu, Lambda) = 3 Rank = 1 For Mu ( 0 , 0 , 0 , 0 ) and Lambda ( 3 , 5 , 4 , 0 ) That's Mu ( 0 , 0 , 0 , 0 ) and Lambda ( 7 , 11 , 10 , 5 ) in Root notation. l(Lambda) = 7; l(Mu) = 0 P(Mu,Lambda) = ( +1 t^0 +2 t^2 +1 t^4 +1 t^6 ) Weyl(Mu, Lambda) = 540 Rank = 110 For Mu ( 3 , 0 , 0 , 3 ) and Lambda ( 3 , 5 , 4 , 0 ) That's Mu ( 3 , 3 , 3 , 3 ) and Lambda ( 7 , 11 , 10 , 5 ) in Root notation. l(Lambda) = 7; l(Mu) = 1 P(Mu,Lambda) = ( +1 t^0 +2 t^2 ) Weyl(Mu, Lambda) = 225 Rank = 60 For Mu ( 4 , 0 , 1 , 2 ) and Lambda ( 3 , 5 , 4 , 0 ) That's Mu ( 4 , 4 , 4 , 3 ) and Lambda ( 7 , 11 , 10 , 5 ) in Root notation. l(Lambda) = 7; l(Mu) = 2 P(Mu,Lambda) = ( +1 t^0 +1 t^2 ) Weyl(Mu, Lambda) = 156 Rank = 47 For Mu ( 2 , 1 , 0 , 4 ) and Lambda ( 3 , 5 , 4 , 0 ) That's Mu ( 3 , 4 , 4 , 4 ) and Lambda ( 7 , 11 , 10 , 5 ) in Root notation. l(Lambda) = 7; l(Mu) = 2 P(Mu,Lambda) = ( +1 t^0 +2 t^2 ) Weyl(Mu, Lambda) = 134 Rank = 43 For Mu ( 5 , 1 , 0 , 2 ) and Lambda ( 3 , 5 , 4 , 0 ) That's Mu ( 5 , 5 , 4 , 3 ) and Lambda ( 7 , 11 , 10 , 5 ) in Root notation. l(Lambda) = 7; l(Mu) = 3 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 91 Rank = 34 For Mu ( 3 , 1 , 1 , 3 ) and Lambda ( 3 , 5 , 4 , 0 ) That's Mu ( 4 , 5 , 5 , 4 ) and Lambda ( 7 , 11 , 10 , 5 ) in Root notation. l(Lambda) = 7; l(Mu) = 3 P(Mu,Lambda) = ( +1 t^0 +1 t^2 ) Weyl(Mu, Lambda) = 95 Rank = 34 For Mu ( 2 , 0 , 1 , 5 ) and Lambda ( 3 , 5 , 4 , 0 ) That's Mu ( 3 , 4 , 5 , 5 ) and Lambda ( 7 , 11 , 10 , 5 ) in Root notation. l(Lambda) = 7; l(Mu) = 3 P(Mu,Lambda) = ( +1 t^0 +2 t^2 ) Weyl(Mu, Lambda) = 52 Rank = 23 For Mu ( 4 , 2 , 0 , 3 ) and Lambda ( 3 , 5 , 4 , 0 ) That's Mu ( 5 , 6 , 5 , 4 ) and Lambda ( 7 , 11 , 10 , 5 ) in Root notation. l(Lambda) = 7; l(Mu) = 4 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 57 Rank = 25 For Mu ( 3 , 0 , 2 , 4 ) and Lambda ( 3 , 5 , 4 , 0 ) That's Mu ( 4 , 5 , 6 , 5 ) and Lambda ( 7 , 11 , 10 , 5 ) in Root notation. l(Lambda) = 7; l(Mu) = 4 P(Mu,Lambda) = ( +1 t^0 +1 t^2 ) Weyl(Mu, Lambda) = 38 Rank = 18 For Mu ( 0 , 4 , 4 , 0 ) and Lambda ( 3 , 5 , 4 , 0 ) That's Mu ( 4 , 8 , 8 , 4 ) and Lambda ( 7 , 11 , 10 , 5 ) in Root notation. l(Lambda) = 7; l(Mu) = 4 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 24 Rank = 12 For Mu ( 5 , 2 , 0 , 4 ) and Lambda ( 3 , 5 , 4 , 0 ) That's Mu ( 6 , 7 , 6 , 5 ) and Lambda ( 7 , 11 , 10 , 5 ) in Root notation. l(Lambda) = 7; l(Mu) = 5 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 13 Rank = 9 For Mu ( 1 , 5 , 3 , 0 ) and Lambda ( 3 , 5 , 4 , 0 ) That's Mu ( 5 , 9 , 8 , 4 ) and Lambda ( 7 , 11 , 10 , 5 ) in Root notation. l(Lambda) = 7; l(Mu) = 5 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 15 Rank = 8 For Mu ( 0 , 3 , 5 , 1 ) and Lambda ( 3 , 5 , 4 , 0 ) That's Mu ( 4 , 8 , 9 , 5 ) and Lambda ( 7 , 11 , 10 , 5 ) in Root notation. l(Lambda) = 7; l(Mu) = 5 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 10 Rank = 7 For Mu ( 2 , 5 , 3 , 1 ) and Lambda ( 3 , 5 , 4 , 0 ) That's Mu ( 6 , 10 , 9 , 5 ) and Lambda ( 7 , 11 , 10 , 5 ) in Root notation. l(Lambda) = 7; l(Mu) = 6 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 4 Rank = 3 For Mu ( 3 , 5 , 4 , 0 ) and Lambda ( 3 , 5 , 4 , 0 ) That's Mu ( 7 , 11 , 10 , 5 ) and Lambda ( 7 , 11 , 10 , 5 ) in Root notation. l(Lambda) = 7; l(Mu) = 7 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 1 Rank = 1 For Mu ( 7 , 0 , 0 , 2 ) and Lambda ( 3 , 5 , 4 , 0 ) That's Mu ( 6 , 5 , 4 , 3 ) and Lambda ( 7 , 11 , 10 , 5 ) in Root notation. l(Lambda) = 7; l(Mu) = 4 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 42 Rank = 21 For Mu ( 7 , 1 , 0 , 4 ) and Lambda ( 3 , 5 , 4 , 0 ) That's Mu ( 7 , 7 , 6 , 5 ) and Lambda ( 7 , 11 , 10 , 5 ) in Root notation. l(Lambda) = 7; l(Mu) = 6 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 5 Rank = 4 For Mu ( 0 , 7 , 2 , 0 ) and Lambda ( 3 , 5 , 4 , 0 ) That's Mu ( 5 , 10 , 8 , 4 ) and Lambda ( 7 , 11 , 10 , 5 ) in Root notation. l(Lambda) = 7; l(Mu) = 6 P(Mu,Lambda) = ( ) Weyl(Mu, Lambda) = 6 Rank = 4 For Mu ( 0 , 2 , 7 , 0 ) and Lambda ( 3 , 5 , 4 , 0 ) That's Mu ( 4 , 8 , 10 , 5 ) and Lambda ( 7 , 11 , 10 , 5 ) in Root notation. l(Lambda) = 7; l(Mu) = 6 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 4 Rank = 3 For Mu ( 1 , 7 , 2 , 1 ) and Lambda ( 3 , 5 , 4 , 0 ) That's Mu ( 6 , 11 , 9 , 5 ) and Lambda ( 7 , 11 , 10 , 5 ) in Root notation. l(Lambda) = 7; l(Mu) = 7 P(Mu,Lambda) = ( ) Weyl(Mu, Lambda) = 1 Rank = 1 For Mu ( 8 , 0 , 0 , 3 ) and Lambda ( 3 , 5 , 4 , 0 ) That's Mu ( 7 , 6 , 5 , 4 ) and Lambda ( 7 , 11 , 10 , 5 ) in Root notation. l(Lambda) = 7; l(Mu) = 5 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 9 Rank = 7 For Mu ( 0 , 0 , 0 , 0 ) and Lambda ( 0 , 4 , 5 , 3 ) That's Mu ( 0 , 0 , 0 , 0 ) and Lambda ( 5 , 10 , 11 , 7 ) in Root notation. l(Lambda) = 7; l(Mu) = 0 P(Mu,Lambda) = ( +1 t^0 +2 t^2 +1 t^4 +1 t^6 ) Weyl(Mu, Lambda) = 540 Rank = 110 For Mu ( 3 , 0 , 0 , 3 ) and Lambda ( 0 , 4 , 5 , 3 ) That's Mu ( 3 , 3 , 3 , 3 ) and Lambda ( 5 , 10 , 11 , 7 ) in Root notation. l(Lambda) = 7; l(Mu) = 1 P(Mu,Lambda) = ( +1 t^0 +2 t^2 ) Weyl(Mu, Lambda) = 225 Rank = 60 For Mu ( 4 , 0 , 1 , 2 ) and Lambda ( 0 , 4 , 5 , 3 ) That's Mu ( 4 , 4 , 4 , 3 ) and Lambda ( 5 , 10 , 11 , 7 ) in Root notation. l(Lambda) = 7; l(Mu) = 2 P(Mu,Lambda) = ( +1 t^0 +2 t^2 ) Weyl(Mu, Lambda) = 134 Rank = 43 For Mu ( 2 , 1 , 0 , 4 ) and Lambda ( 0 , 4 , 5 , 3 ) That's Mu ( 3 , 4 , 4 , 4 ) and Lambda ( 5 , 10 , 11 , 7 ) in Root notation. l(Lambda) = 7; l(Mu) = 2 P(Mu,Lambda) = ( +1 t^0 +1 t^2 ) Weyl(Mu, Lambda) = 156 Rank = 47 For Mu ( 5 , 1 , 0 , 2 ) and Lambda ( 0 , 4 , 5 , 3 ) That's Mu ( 5 , 5 , 4 , 3 ) and Lambda ( 5 , 10 , 11 , 7 ) in Root notation. l(Lambda) = 7; l(Mu) = 3 P(Mu,Lambda) = ( +1 t^0 +2 t^2 ) Weyl(Mu, Lambda) = 52 Rank = 23 For Mu ( 3 , 1 , 1 , 3 ) and Lambda ( 0 , 4 , 5 , 3 ) That's Mu ( 4 , 5 , 5 , 4 ) and Lambda ( 5 , 10 , 11 , 7 ) in Root notation. l(Lambda) = 7; l(Mu) = 3 P(Mu,Lambda) = ( +1 t^0 +1 t^2 ) Weyl(Mu, Lambda) = 95 Rank = 34 For Mu ( 2 , 0 , 1 , 5 ) and Lambda ( 0 , 4 , 5 , 3 ) That's Mu ( 3 , 4 , 5 , 5 ) and Lambda ( 5 , 10 , 11 , 7 ) in Root notation. l(Lambda) = 7; l(Mu) = 3 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 91 Rank = 34 For Mu ( 4 , 2 , 0 , 3 ) and Lambda ( 0 , 4 , 5 , 3 ) That's Mu ( 5 , 6 , 5 , 4 ) and Lambda ( 5 , 10 , 11 , 7 ) in Root notation. l(Lambda) = 7; l(Mu) = 4 P(Mu,Lambda) = ( +1 t^0 +1 t^2 ) Weyl(Mu, Lambda) = 38 Rank = 18 For Mu ( 3 , 0 , 2 , 4 ) and Lambda ( 0 , 4 , 5 , 3 ) That's Mu ( 4 , 5 , 6 , 5 ) and Lambda ( 5 , 10 , 11 , 7 ) in Root notation. l(Lambda) = 7; l(Mu) = 4 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 57 Rank = 25 For Mu ( 0 , 4 , 4 , 0 ) and Lambda ( 0 , 4 , 5 , 3 ) That's Mu ( 4 , 8 , 8 , 4 ) and Lambda ( 5 , 10 , 11 , 7 ) in Root notation. l(Lambda) = 7; l(Mu) = 4 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 24 Rank = 12 For Mu ( 1 , 5 , 3 , 0 ) and Lambda ( 0 , 4 , 5 , 3 ) That's Mu ( 5 , 9 , 8 , 4 ) and Lambda ( 5 , 10 , 11 , 7 ) in Root notation. l(Lambda) = 7; l(Mu) = 5 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 10 Rank = 7 For Mu ( 4 , 0 , 2 , 5 ) and Lambda ( 0 , 4 , 5 , 3 ) That's Mu ( 5 , 6 , 7 , 6 ) and Lambda ( 5 , 10 , 11 , 7 ) in Root notation. l(Lambda) = 7; l(Mu) = 5 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 13 Rank = 9 For Mu ( 0 , 3 , 5 , 1 ) and Lambda ( 0 , 4 , 5 , 3 ) That's Mu ( 4 , 8 , 9 , 5 ) and Lambda ( 5 , 10 , 11 , 7 ) in Root notation. l(Lambda) = 7; l(Mu) = 5 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 15 Rank = 8 For Mu ( 1 , 3 , 5 , 2 ) and Lambda ( 0 , 4 , 5 , 3 ) That's Mu ( 5 , 9 , 10 , 6 ) and Lambda ( 5 , 10 , 11 , 7 ) in Root notation. l(Lambda) = 7; l(Mu) = 6 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 4 Rank = 3 For Mu ( 0 , 4 , 5 , 3 ) and Lambda ( 0 , 4 , 5 , 3 ) That's Mu ( 5 , 10 , 11 , 7 ) and Lambda ( 5 , 10 , 11 , 7 ) in Root notation. l(Lambda) = 7; l(Mu) = 7 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 1 Rank = 1 For Mu ( 2 , 0 , 0 , 7 ) and Lambda ( 0 , 4 , 5 , 3 ) That's Mu ( 3 , 4 , 5 , 6 ) and Lambda ( 5 , 10 , 11 , 7 ) in Root notation. l(Lambda) = 7; l(Mu) = 4 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 42 Rank = 21 For Mu ( 0 , 7 , 2 , 0 ) and Lambda ( 0 , 4 , 5 , 3 ) That's Mu ( 5 , 10 , 8 , 4 ) and Lambda ( 5 , 10 , 11 , 7 ) in Root notation. l(Lambda) = 7; l(Mu) = 6 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 4 Rank = 3 For Mu ( 4 , 0 , 1 , 7 ) and Lambda ( 0 , 4 , 5 , 3 ) That's Mu ( 5 , 6 , 7 , 7 ) and Lambda ( 5 , 10 , 11 , 7 ) in Root notation. l(Lambda) = 7; l(Mu) = 6 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 5 Rank = 4 For Mu ( 0 , 2 , 7 , 0 ) and Lambda ( 0 , 4 , 5 , 3 ) That's Mu ( 4 , 8 , 10 , 5 ) and Lambda ( 5 , 10 , 11 , 7 ) in Root notation. l(Lambda) = 7; l(Mu) = 6 P(Mu,Lambda) = ( ) Weyl(Mu, Lambda) = 6 Rank = 4 For Mu ( 1 , 2 , 7 , 1 ) and Lambda ( 0 , 4 , 5 , 3 ) That's Mu ( 5 , 9 , 11 , 6 ) and Lambda ( 5 , 10 , 11 , 7 ) in Root notation. l(Lambda) = 7; l(Mu) = 7 P(Mu,Lambda) = ( ) Weyl(Mu, Lambda) = 1 Rank = 1 For Mu ( 3 , 0 , 0 , 8 ) and Lambda ( 0 , 4 , 5 , 3 ) That's Mu ( 4 , 5 , 6 , 7 ) and Lambda ( 5 , 10 , 11 , 7 ) in Root notation. l(Lambda) = 7; l(Mu) = 5 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 9 Rank = 7 For Mu ( 0 , 0 , 0 , 0 ) and Lambda ( 1 , 5 , 4 , 3 ) That's Mu ( 0 , 0 , 0 , 0 ) and Lambda ( 6 , 11 , 11 , 7 ) in Root notation. l(Lambda) = 8; l(Mu) = 0 P(Mu,Lambda) = ( +1 t^0 +3 t^2 +3 t^4 +2 t^6 ) Weyl(Mu, Lambda) = 1340 Rank = 220 For Mu ( 3 , 0 , 0 , 3 ) and Lambda ( 1 , 5 , 4 , 3 ) That's Mu ( 3 , 3 , 3 , 3 ) and Lambda ( 6 , 11 , 11 , 7 ) in Root notation. l(Lambda) = 8; l(Mu) = 1 P(Mu,Lambda) = ( +1 t^0 +3 t^2 +2 t^4 ) Weyl(Mu, Lambda) = 586 Rank = 120 For Mu ( 4 , 0 , 1 , 2 ) and Lambda ( 1 , 5 , 4 , 3 ) That's Mu ( 4 , 4 , 4 , 3 ) and Lambda ( 6 , 11 , 11 , 7 ) in Root notation. l(Lambda) = 8; l(Mu) = 2 P(Mu,Lambda) = ( +1 t^0 +3 t^2 +2 t^4 ) Weyl(Mu, Lambda) = 385 Rank = 91 For Mu ( 2 , 1 , 0 , 4 ) and Lambda ( 1 , 5 , 4 , 3 ) That's Mu ( 3 , 4 , 4 , 4 ) and Lambda ( 6 , 11 , 11 , 7 ) in Root notation. l(Lambda) = 8; l(Mu) = 2 P(Mu,Lambda) = ( +1 t^0 +2 t^2 ) Weyl(Mu, Lambda) = 396 Rank = 94 For Mu ( 5 , 1 , 0 , 2 ) and Lambda ( 1 , 5 , 4 , 3 ) That's Mu ( 5 , 5 , 4 , 3 ) and Lambda ( 6 , 11 , 11 , 7 ) in Root notation. l(Lambda) = 8; l(Mu) = 3 P(Mu,Lambda) = ( +1 t^0 +2 t^2 ) Weyl(Mu, Lambda) = 196 Rank = 57 For Mu ( 3 , 1 , 1 , 3 ) and Lambda ( 1 , 5 , 4 , 3 ) That's Mu ( 4 , 5 , 5 , 4 ) and Lambda ( 6 , 11 , 11 , 7 ) in Root notation. l(Lambda) = 8; l(Mu) = 3 P(Mu,Lambda) = ( +1 t^0 +2 t^2 ) Weyl(Mu, Lambda) = 263 Rank = 71 For Mu ( 2 , 0 , 1 , 5 ) and Lambda ( 1 , 5 , 4 , 3 ) That's Mu ( 3 , 4 , 5 , 5 ) and Lambda ( 6 , 11 , 11 , 7 ) in Root notation. l(Lambda) = 8; l(Mu) = 3 P(Mu,Lambda) = ( +1 t^0 +2 t^2 ) Weyl(Mu, Lambda) = 222 Rank = 67 For Mu ( 4 , 2 , 0 , 3 ) and Lambda ( 1 , 5 , 4 , 3 ) That's Mu ( 5 , 6 , 5 , 4 ) and Lambda ( 6 , 11 , 11 , 7 ) in Root notation. l(Lambda) = 8; l(Mu) = 4 P(Mu,Lambda) = ( +1 t^0 +1 t^2 ) Weyl(Mu, Lambda) = 136 Rank = 45 For Mu ( 3 , 0 , 2 , 4 ) and Lambda ( 1 , 5 , 4 , 3 ) That's Mu ( 4 , 5 , 6 , 5 ) and Lambda ( 6 , 11 , 11 , 7 ) in Root notation. l(Lambda) = 8; l(Mu) = 4 P(Mu,Lambda) = ( +1 t^0 +2 t^2 ) Weyl(Mu, Lambda) = 148 Rank = 50 For Mu ( 0 , 4 , 4 , 0 ) and Lambda ( 1 , 5 , 4 , 3 ) That's Mu ( 4 , 8 , 8 , 4 ) and Lambda ( 6 , 11 , 11 , 7 ) in Root notation. l(Lambda) = 8; l(Mu) = 4 P(Mu,Lambda) = ( +1 t^0 +1 t^2 ) Weyl(Mu, Lambda) = 72 Rank = 26 For Mu ( 5 , 2 , 0 , 4 ) and Lambda ( 1 , 5 , 4 , 3 ) That's Mu ( 6 , 7 , 6 , 5 ) and Lambda ( 6 , 11 , 11 , 7 ) in Root notation. l(Lambda) = 8; l(Mu) = 5 P(Mu,Lambda) = ( +1 t^0 +1 t^2 ) Weyl(Mu, Lambda) = 24 Rank = 13 For Mu ( 1 , 5 , 3 , 0 ) and Lambda ( 1 , 5 , 4 , 3 ) That's Mu ( 5 , 9 , 8 , 4 ) and Lambda ( 6 , 11 , 11 , 7 ) in Root notation. l(Lambda) = 8; l(Mu) = 5 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 40 Rank = 17 For Mu ( 4 , 0 , 2 , 5 ) and Lambda ( 1 , 5 , 4 , 3 ) That's Mu ( 5 , 6 , 7 , 6 ) and Lambda ( 6 , 11 , 11 , 7 ) in Root notation. l(Lambda) = 8; l(Mu) = 5 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 40 Rank = 20 For Mu ( 0 , 3 , 5 , 1 ) and Lambda ( 1 , 5 , 4 , 3 ) That's Mu ( 4 , 8 , 9 , 5 ) and Lambda ( 6 , 11 , 11 , 7 ) in Root notation. l(Lambda) = 8; l(Mu) = 5 P(Mu,Lambda) = ( +1 t^0 +1 t^2 ) Weyl(Mu, Lambda) = 36 Rank = 14 For Mu ( 5 , 1 , 1 , 5 ) and Lambda ( 1 , 5 , 4 , 3 ) That's Mu ( 6 , 7 , 7 , 6 ) and Lambda ( 6 , 11 , 11 , 7 ) in Root notation. l(Lambda) = 8; l(Mu) = 6 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 13 Rank = 9 For Mu ( 2 , 5 , 3 , 1 ) and Lambda ( 1 , 5 , 4 , 3 ) That's Mu ( 6 , 10 , 9 , 5 ) and Lambda ( 6 , 11 , 11 , 7 ) in Root notation. l(Lambda) = 8; l(Mu) = 6 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 7 Rank = 5 For Mu ( 1 , 3 , 5 , 2 ) and Lambda ( 1 , 5 , 4 , 3 ) That's Mu ( 5 , 9 , 10 , 6 ) and Lambda ( 6 , 11 , 11 , 7 ) in Root notation. l(Lambda) = 8; l(Mu) = 6 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 10 Rank = 5 For Mu ( 2 , 4 , 4 , 2 ) and Lambda ( 1 , 5 , 4 , 3 ) That's Mu ( 6 , 10 , 10 , 6 ) and Lambda ( 6 , 11 , 11 , 7 ) in Root notation. l(Lambda) = 8; l(Mu) = 7 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 4 Rank = 3 For Mu ( 0 , 4 , 5 , 3 ) and Lambda ( 1 , 5 , 4 , 3 ) That's Mu ( 5 , 10 , 11 , 7 ) and Lambda ( 6 , 11 , 11 , 7 ) in Root notation. l(Lambda) = 8; l(Mu) = 7 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 2 Rank = 1 For Mu ( 1 , 5 , 4 , 3 ) and Lambda ( 1 , 5 , 4 , 3 ) That's Mu ( 6 , 11 , 11 , 7 ) and Lambda ( 6 , 11 , 11 , 7 ) in Root notation. l(Lambda) = 8; l(Mu) = 8 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 1 Rank = 1 For Mu ( 7 , 0 , 0 , 2 ) and Lambda ( 1 , 5 , 4 , 3 ) That's Mu ( 6 , 5 , 4 , 3 ) and Lambda ( 6 , 11 , 11 , 7 ) in Root notation. l(Lambda) = 8; l(Mu) = 4 P(Mu,Lambda) = ( +1 t^0 +2 t^2 ) Weyl(Mu, Lambda) = 54 Rank = 22 For Mu ( 2 , 0 , 0 , 7 ) and Lambda ( 1 , 5 , 4 , 3 ) That's Mu ( 3 , 4 , 5 , 6 ) and Lambda ( 6 , 11 , 11 , 7 ) in Root notation. l(Lambda) = 8; l(Mu) = 4 P(Mu,Lambda) = ( +1 t^0 +1 t^2 ) Weyl(Mu, Lambda) = 100 Rank = 39 For Mu ( 0 , 7 , 2 , 0 ) and Lambda ( 1 , 5 , 4 , 3 ) That's Mu ( 5 , 10 , 8 , 4 ) and Lambda ( 6 , 11 , 11 , 7 ) in Root notation. l(Lambda) = 8; l(Mu) = 6 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 20 Rank = 8 For Mu ( 4 , 0 , 1 , 7 ) and Lambda ( 1 , 5 , 4 , 3 ) That's Mu ( 5 , 6 , 7 , 7 ) and Lambda ( 6 , 11 , 11 , 7 ) in Root notation. l(Lambda) = 8; l(Mu) = 6 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 14 Rank = 8 For Mu ( 0 , 2 , 7 , 0 ) and Lambda ( 1 , 5 , 4 , 3 ) That's Mu ( 4 , 8 , 10 , 5 ) and Lambda ( 6 , 11 , 11 , 7 ) in Root notation. l(Lambda) = 8; l(Mu) = 6 P(Mu,Lambda) = ( ) Weyl(Mu, Lambda) = 12 Rank = 5 For Mu ( 5 , 1 , 0 , 7 ) and Lambda ( 1 , 5 , 4 , 3 ) That's Mu ( 6 , 7 , 7 , 7 ) and Lambda ( 6 , 11 , 11 , 7 ) in Root notation. l(Lambda) = 8; l(Mu) = 7 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 5 Rank = 4 For Mu ( 1 , 7 , 2 , 1 ) and Lambda ( 1 , 5 , 4 , 3 ) That's Mu ( 6 , 11 , 9 , 5 ) and Lambda ( 6 , 11 , 11 , 7 ) in Root notation. l(Lambda) = 8; l(Mu) = 7 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 3 Rank = 2 For Mu ( 1 , 2 , 7 , 1 ) and Lambda ( 1 , 5 , 4 , 3 ) That's Mu ( 5 , 9 , 11 , 6 ) and Lambda ( 6 , 11 , 11 , 7 ) in Root notation. l(Lambda) = 8; l(Mu) = 7 P(Mu,Lambda) = ( ) Weyl(Mu, Lambda) = 2 Rank = 1 For Mu ( 3 , 0 , 0 , 8 ) and Lambda ( 1 , 5 , 4 , 3 ) That's Mu ( 4 , 5 , 6 , 7 ) and Lambda ( 6 , 11 , 11 , 7 ) in Root notation. l(Lambda) = 8; l(Mu) = 5 P(Mu,Lambda) = ( +1 t^0 +1 t^2 ) Weyl(Mu, Lambda) = 22 Rank = 11 For Mu ( 0 , 0 , 0 , 0 ) and Lambda ( 3 , 4 , 5 , 1 ) That's Mu ( 0 , 0 , 0 , 0 ) and Lambda ( 7 , 11 , 11 , 6 ) in Root notation. l(Lambda) = 8; l(Mu) = 0 P(Mu,Lambda) = ( +1 t^0 +3 t^2 +3 t^4 +2 t^6 ) Weyl(Mu, Lambda) = 1340 Rank = 220 For Mu ( 3 , 0 , 0 , 3 ) and Lambda ( 3 , 4 , 5 , 1 ) That's Mu ( 3 , 3 , 3 , 3 ) and Lambda ( 7 , 11 , 11 , 6 ) in Root notation. l(Lambda) = 8; l(Mu) = 1 P(Mu,Lambda) = ( +1 t^0 +3 t^2 +2 t^4 ) Weyl(Mu, Lambda) = 586 Rank = 120 For Mu ( 4 , 0 , 1 , 2 ) and Lambda ( 3 , 4 , 5 , 1 ) That's Mu ( 4 , 4 , 4 , 3 ) and Lambda ( 7 , 11 , 11 , 6 ) in Root notation. l(Lambda) = 8; l(Mu) = 2 P(Mu,Lambda) = ( +1 t^0 +2 t^2 ) Weyl(Mu, Lambda) = 396 Rank = 94 For Mu ( 2 , 1 , 0 , 4 ) and Lambda ( 3 , 4 , 5 , 1 ) That's Mu ( 3 , 4 , 4 , 4 ) and Lambda ( 7 , 11 , 11 , 6 ) in Root notation. l(Lambda) = 8; l(Mu) = 2 P(Mu,Lambda) = ( +1 t^0 +3 t^2 +2 t^4 ) Weyl(Mu, Lambda) = 385 Rank = 91 For Mu ( 5 , 1 , 0 , 2 ) and Lambda ( 3 , 4 , 5 , 1 ) That's Mu ( 5 , 5 , 4 , 3 ) and Lambda ( 7 , 11 , 11 , 6 ) in Root notation. l(Lambda) = 8; l(Mu) = 3 P(Mu,Lambda) = ( +1 t^0 +2 t^2 ) Weyl(Mu, Lambda) = 222 Rank = 67 For Mu ( 3 , 1 , 1 , 3 ) and Lambda ( 3 , 4 , 5 , 1 ) That's Mu ( 4 , 5 , 5 , 4 ) and Lambda ( 7 , 11 , 11 , 6 ) in Root notation. l(Lambda) = 8; l(Mu) = 3 P(Mu,Lambda) = ( +1 t^0 +2 t^2 ) Weyl(Mu, Lambda) = 263 Rank = 71 For Mu ( 2 , 0 , 1 , 5 ) and Lambda ( 3 , 4 , 5 , 1 ) That's Mu ( 3 , 4 , 5 , 5 ) and Lambda ( 7 , 11 , 11 , 6 ) in Root notation. l(Lambda) = 8; l(Mu) = 3 P(Mu,Lambda) = ( +1 t^0 +2 t^2 ) Weyl(Mu, Lambda) = 196 Rank = 57 For Mu ( 4 , 2 , 0 , 3 ) and Lambda ( 3 , 4 , 5 , 1 ) That's Mu ( 5 , 6 , 5 , 4 ) and Lambda ( 7 , 11 , 11 , 6 ) in Root notation. l(Lambda) = 8; l(Mu) = 4 P(Mu,Lambda) = ( +1 t^0 +2 t^2 ) Weyl(Mu, Lambda) = 148 Rank = 50 For Mu ( 3 , 0 , 2 , 4 ) and Lambda ( 3 , 4 , 5 , 1 ) That's Mu ( 4 , 5 , 6 , 5 ) and Lambda ( 7 , 11 , 11 , 6 ) in Root notation. l(Lambda) = 8; l(Mu) = 4 P(Mu,Lambda) = ( +1 t^0 +1 t^2 ) Weyl(Mu, Lambda) = 136 Rank = 45 For Mu ( 0 , 4 , 4 , 0 ) and Lambda ( 3 , 4 , 5 , 1 ) That's Mu ( 4 , 8 , 8 , 4 ) and Lambda ( 7 , 11 , 11 , 6 ) in Root notation. l(Lambda) = 8; l(Mu) = 4 P(Mu,Lambda) = ( +1 t^0 +1 t^2 ) Weyl(Mu, Lambda) = 72 Rank = 26 For Mu ( 5 , 2 , 0 , 4 ) and Lambda ( 3 , 4 , 5 , 1 ) That's Mu ( 6 , 7 , 6 , 5 ) and Lambda ( 7 , 11 , 11 , 6 ) in Root notation. l(Lambda) = 8; l(Mu) = 5 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 40 Rank = 20 For Mu ( 1 , 5 , 3 , 0 ) and Lambda ( 3 , 4 , 5 , 1 ) That's Mu ( 5 , 9 , 8 , 4 ) and Lambda ( 7 , 11 , 11 , 6 ) in Root notation. l(Lambda) = 8; l(Mu) = 5 P(Mu,Lambda) = ( +1 t^0 +1 t^2 ) Weyl(Mu, Lambda) = 36 Rank = 14 For Mu ( 4 , 0 , 2 , 5 ) and Lambda ( 3 , 4 , 5 , 1 ) That's Mu ( 5 , 6 , 7 , 6 ) and Lambda ( 7 , 11 , 11 , 6 ) in Root notation. l(Lambda) = 8; l(Mu) = 5 P(Mu,Lambda) = ( +1 t^0 +1 t^2 ) Weyl(Mu, Lambda) = 24 Rank = 13 For Mu ( 0 , 3 , 5 , 1 ) and Lambda ( 3 , 4 , 5 , 1 ) That's Mu ( 4 , 8 , 9 , 5 ) and Lambda ( 7 , 11 , 11 , 6 ) in Root notation. l(Lambda) = 8; l(Mu) = 5 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 40 Rank = 17 For Mu ( 5 , 1 , 1 , 5 ) and Lambda ( 3 , 4 , 5 , 1 ) That's Mu ( 6 , 7 , 7 , 6 ) and Lambda ( 7 , 11 , 11 , 6 ) in Root notation. l(Lambda) = 8; l(Mu) = 6 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 13 Rank = 9 For Mu ( 2 , 5 , 3 , 1 ) and Lambda ( 3 , 4 , 5 , 1 ) That's Mu ( 6 , 10 , 9 , 5 ) and Lambda ( 7 , 11 , 11 , 6 ) in Root notation. l(Lambda) = 8; l(Mu) = 6 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 10 Rank = 5 For Mu ( 1 , 3 , 5 , 2 ) and Lambda ( 3 , 4 , 5 , 1 ) That's Mu ( 5 , 9 , 10 , 6 ) and Lambda ( 7 , 11 , 11 , 6 ) in Root notation. l(Lambda) = 8; l(Mu) = 6 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 7 Rank = 5 For Mu ( 2 , 4 , 4 , 2 ) and Lambda ( 3 , 4 , 5 , 1 ) That's Mu ( 6 , 10 , 10 , 6 ) and Lambda ( 7 , 11 , 11 , 6 ) in Root notation. l(Lambda) = 8; l(Mu) = 7 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 4 Rank = 3 For Mu ( 3 , 5 , 4 , 0 ) and Lambda ( 3 , 4 , 5 , 1 ) That's Mu ( 7 , 11 , 10 , 5 ) and Lambda ( 7 , 11 , 11 , 6 ) in Root notation. l(Lambda) = 8; l(Mu) = 7 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 2 Rank = 1 For Mu ( 3 , 4 , 5 , 1 ) and Lambda ( 3 , 4 , 5 , 1 ) That's Mu ( 7 , 11 , 11 , 6 ) and Lambda ( 7 , 11 , 11 , 6 ) in Root notation. l(Lambda) = 8; l(Mu) = 8 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 1 Rank = 1 For Mu ( 7 , 0 , 0 , 2 ) and Lambda ( 3 , 4 , 5 , 1 ) That's Mu ( 6 , 5 , 4 , 3 ) and Lambda ( 7 , 11 , 11 , 6 ) in Root notation. l(Lambda) = 8; l(Mu) = 4 P(Mu,Lambda) = ( +1 t^0 +1 t^2 ) Weyl(Mu, Lambda) = 100 Rank = 39 For Mu ( 2 , 0 , 0 , 7 ) and Lambda ( 3 , 4 , 5 , 1 ) That's Mu ( 3 , 4 , 5 , 6 ) and Lambda ( 7 , 11 , 11 , 6 ) in Root notation. l(Lambda) = 8; l(Mu) = 4 P(Mu,Lambda) = ( +1 t^0 +2 t^2 ) Weyl(Mu, Lambda) = 54 Rank = 22 For Mu ( 7 , 1 , 0 , 4 ) and Lambda ( 3 , 4 , 5 , 1 ) That's Mu ( 7 , 7 , 6 , 5 ) and Lambda ( 7 , 11 , 11 , 6 ) in Root notation. l(Lambda) = 8; l(Mu) = 6 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 14 Rank = 8 For Mu ( 0 , 7 , 2 , 0 ) and Lambda ( 3 , 4 , 5 , 1 ) That's Mu ( 5 , 10 , 8 , 4 ) and Lambda ( 7 , 11 , 11 , 6 ) in Root notation. l(Lambda) = 8; l(Mu) = 6 P(Mu,Lambda) = ( ) Weyl(Mu, Lambda) = 12 Rank = 5 For Mu ( 0 , 2 , 7 , 0 ) and Lambda ( 3 , 4 , 5 , 1 ) That's Mu ( 4 , 8 , 10 , 5 ) and Lambda ( 7 , 11 , 11 , 6 ) in Root notation. l(Lambda) = 8; l(Mu) = 6 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 20 Rank = 8 For Mu ( 7 , 0 , 1 , 5 ) and Lambda ( 3 , 4 , 5 , 1 ) That's Mu ( 7 , 7 , 7 , 6 ) and Lambda ( 7 , 11 , 11 , 6 ) in Root notation. l(Lambda) = 8; l(Mu) = 7 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 5 Rank = 4 For Mu ( 1 , 7 , 2 , 1 ) and Lambda ( 3 , 4 , 5 , 1 ) That's Mu ( 6 , 11 , 9 , 5 ) and Lambda ( 7 , 11 , 11 , 6 ) in Root notation. l(Lambda) = 8; l(Mu) = 7 P(Mu,Lambda) = ( ) Weyl(Mu, Lambda) = 2 Rank = 1 For Mu ( 1 , 2 , 7 , 1 ) and Lambda ( 3 , 4 , 5 , 1 ) That's Mu ( 5 , 9 , 11 , 6 ) and Lambda ( 7 , 11 , 11 , 6 ) in Root notation. l(Lambda) = 8; l(Mu) = 7 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 3 Rank = 2 For Mu ( 8 , 0 , 0 , 3 ) and Lambda ( 3 , 4 , 5 , 1 ) That's Mu ( 7 , 6 , 5 , 4 ) and Lambda ( 7 , 11 , 11 , 6 ) in Root notation. l(Lambda) = 8; l(Mu) = 5 P(Mu,Lambda) = ( +1 t^0 +1 t^2 ) Weyl(Mu, Lambda) = 22 Rank = 11 For Mu ( 0 , 0 , 0 , 0 ) and Lambda ( 2 , 5 , 5 , 2 ) That's Mu ( 0 , 0 , 0 , 0 ) and Lambda ( 7 , 12 , 12 , 7 ) in Root notation. l(Lambda) = 9; l(Mu) = 0 P(Mu,Lambda) = ( +1 t^0 +4 t^2 +5 t^4 +4 t^6 +2 t^8 ) Weyl(Mu, Lambda) = 2085 Rank = 425 For Mu ( 3 , 0 , 0 , 3 ) and Lambda ( 2 , 5 , 5 , 2 ) That's Mu ( 3 , 3 , 3 , 3 ) and Lambda ( 7 , 12 , 12 , 7 ) in Root notation. l(Lambda) = 9; l(Mu) = 1 P(Mu,Lambda) = ( +1 t^0 +4 t^2 +3 t^4 ) Weyl(Mu, Lambda) = 1008 Rank = 233 For Mu ( 4 , 0 , 1 , 2 ) and Lambda ( 2 , 5 , 5 , 2 ) That's Mu ( 4 , 4 , 4 , 3 ) and Lambda ( 7 , 12 , 12 , 7 ) in Root notation. l(Lambda) = 9; l(Mu) = 2 P(Mu,Lambda) = ( +1 t^0 +4 t^2 +3 t^4 ) Weyl(Mu, Lambda) = 712 Rank = 179 For Mu ( 2 , 1 , 0 , 4 ) and Lambda ( 2 , 5 , 5 , 2 ) That's Mu ( 3 , 4 , 4 , 4 ) and Lambda ( 7 , 12 , 12 , 7 ) in Root notation. l(Lambda) = 9; l(Mu) = 2 P(Mu,Lambda) = ( +1 t^0 +4 t^2 +3 t^4 ) Weyl(Mu, Lambda) = 712 Rank = 179 For Mu ( 5 , 1 , 0 , 2 ) and Lambda ( 2 , 5 , 5 , 2 ) That's Mu ( 5 , 5 , 4 , 3 ) and Lambda ( 7 , 12 , 12 , 7 ) in Root notation. l(Lambda) = 9; l(Mu) = 3 P(Mu,Lambda) = ( +1 t^0 +3 t^2 +1 t^4 ) Weyl(Mu, Lambda) = 423 Rank = 123 For Mu ( 3 , 1 , 1 , 3 ) and Lambda ( 2 , 5 , 5 , 2 ) That's Mu ( 4 , 5 , 5 , 4 ) and Lambda ( 7 , 12 , 12 , 7 ) in Root notation. l(Lambda) = 9; l(Mu) = 3 P(Mu,Lambda) = ( +1 t^0 +4 t^2 +3 t^4 ) Weyl(Mu, Lambda) = 512 Rank = 141 For Mu ( 2 , 0 , 1 , 5 ) and Lambda ( 2 , 5 , 5 , 2 ) That's Mu ( 3 , 4 , 5 , 5 ) and Lambda ( 7 , 12 , 12 , 7 ) in Root notation. l(Lambda) = 9; l(Mu) = 3 P(Mu,Lambda) = ( +1 t^0 +3 t^2 +1 t^4 ) Weyl(Mu, Lambda) = 423 Rank = 123 For Mu ( 4 , 2 , 0 , 3 ) and Lambda ( 2 , 5 , 5 , 2 ) That's Mu ( 5 , 6 , 5 , 4 ) and Lambda ( 7 , 12 , 12 , 7 ) in Root notation. l(Lambda) = 9; l(Mu) = 4 P(Mu,Lambda) = ( +1 t^0 +3 t^2 +1 t^4 ) Weyl(Mu, Lambda) = 309 Rank = 98 For Mu ( 3 , 0 , 2 , 4 ) and Lambda ( 2 , 5 , 5 , 2 ) That's Mu ( 4 , 5 , 6 , 5 ) and Lambda ( 7 , 12 , 12 , 7 ) in Root notation. l(Lambda) = 9; l(Mu) = 4 P(Mu,Lambda) = ( +1 t^0 +3 t^2 +1 t^4 ) Weyl(Mu, Lambda) = 309 Rank = 98 For Mu ( 0 , 4 , 4 , 0 ) and Lambda ( 2 , 5 , 5 , 2 ) That's Mu ( 4 , 8 , 8 , 4 ) and Lambda ( 7 , 12 , 12 , 7 ) in Root notation. l(Lambda) = 9; l(Mu) = 4 P(Mu,Lambda) = ( +1 t^0 +2 t^2 +1 t^4 ) Weyl(Mu, Lambda) = 174 Rank = 59 For Mu ( 5 , 2 , 0 , 4 ) and Lambda ( 2 , 5 , 5 , 2 ) That's Mu ( 6 , 7 , 6 , 5 ) and Lambda ( 7 , 12 , 12 , 7 ) in Root notation. l(Lambda) = 9; l(Mu) = 5 P(Mu,Lambda) = ( +1 t^0 +1 t^2 ) Weyl(Mu, Lambda) = 94 Rank = 41 For Mu ( 1 , 5 , 3 , 0 ) and Lambda ( 2 , 5 , 5 , 2 ) That's Mu ( 5 , 9 , 8 , 4 ) and Lambda ( 7 , 12 , 12 , 7 ) in Root notation. l(Lambda) = 9; l(Mu) = 5 P(Mu,Lambda) = ( +1 t^0 +1 t^2 ) Weyl(Mu, Lambda) = 106 Rank = 41 For Mu ( 4 , 0 , 2 , 5 ) and Lambda ( 2 , 5 , 5 , 2 ) That's Mu ( 5 , 6 , 7 , 6 ) and Lambda ( 7 , 12 , 12 , 7 ) in Root notation. l(Lambda) = 9; l(Mu) = 5 P(Mu,Lambda) = ( +1 t^0 +1 t^2 ) Weyl(Mu, Lambda) = 94 Rank = 41 For Mu ( 0 , 3 , 5 , 1 ) and Lambda ( 2 , 5 , 5 , 2 ) That's Mu ( 4 , 8 , 9 , 5 ) and Lambda ( 7 , 12 , 12 , 7 ) in Root notation. l(Lambda) = 9; l(Mu) = 5 P(Mu,Lambda) = ( +1 t^0 +1 t^2 ) Weyl(Mu, Lambda) = 106 Rank = 41 For Mu ( 5 , 1 , 1 , 5 ) and Lambda ( 2 , 5 , 5 , 2 ) That's Mu ( 6 , 7 , 7 , 6 ) and Lambda ( 7 , 12 , 12 , 7 ) in Root notation. l(Lambda) = 9; l(Mu) = 6 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 48 Rank = 26 For Mu ( 2 , 5 , 3 , 1 ) and Lambda ( 2 , 5 , 5 , 2 ) That's Mu ( 6 , 10 , 9 , 5 ) and Lambda ( 7 , 12 , 12 , 7 ) in Root notation. l(Lambda) = 9; l(Mu) = 6 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 33 Rank = 17 For Mu ( 1 , 3 , 5 , 2 ) and Lambda ( 2 , 5 , 5 , 2 ) That's Mu ( 5 , 9 , 10 , 6 ) and Lambda ( 7 , 12 , 12 , 7 ) in Root notation. l(Lambda) = 9; l(Mu) = 6 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 33 Rank = 17 For Mu ( 2 , 4 , 4 , 2 ) and Lambda ( 2 , 5 , 5 , 2 ) That's Mu ( 6 , 10 , 10 , 6 ) and Lambda ( 7 , 12 , 12 , 7 ) in Root notation. l(Lambda) = 9; l(Mu) = 7 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 18 Rank = 11 For Mu ( 3 , 5 , 4 , 0 ) and Lambda ( 2 , 5 , 5 , 2 ) That's Mu ( 7 , 11 , 10 , 5 ) and Lambda ( 7 , 12 , 12 , 7 ) in Root notation. l(Lambda) = 9; l(Mu) = 7 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 7 Rank = 5 For Mu ( 0 , 4 , 5 , 3 ) and Lambda ( 2 , 5 , 5 , 2 ) That's Mu ( 5 , 10 , 11 , 7 ) and Lambda ( 7 , 12 , 12 , 7 ) in Root notation. l(Lambda) = 9; l(Mu) = 7 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 7 Rank = 5 For Mu ( 1 , 5 , 4 , 3 ) and Lambda ( 2 , 5 , 5 , 2 ) That's Mu ( 6 , 11 , 11 , 7 ) and Lambda ( 7 , 12 , 12 , 7 ) in Root notation. l(Lambda) = 9; l(Mu) = 8 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 4 Rank = 3 For Mu ( 3 , 4 , 5 , 1 ) and Lambda ( 2 , 5 , 5 , 2 ) That's Mu ( 7 , 11 , 11 , 6 ) and Lambda ( 7 , 12 , 12 , 7 ) in Root notation. l(Lambda) = 9; l(Mu) = 8 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 4 Rank = 3 For Mu ( 2 , 5 , 5 , 2 ) and Lambda ( 2 , 5 , 5 , 2 ) That's Mu ( 7 , 12 , 12 , 7 ) and Lambda ( 7 , 12 , 12 , 7 ) in Root notation. l(Lambda) = 9; l(Mu) = 9 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 1 Rank = 1 For Mu ( 7 , 0 , 0 , 2 ) and Lambda ( 2 , 5 , 5 , 2 ) That's Mu ( 6 , 5 , 4 , 3 ) and Lambda ( 7 , 12 , 12 , 7 ) in Root notation. l(Lambda) = 9; l(Mu) = 4 P(Mu,Lambda) = ( +1 t^0 +2 t^2 ) Weyl(Mu, Lambda) = 186 Rank = 68 For Mu ( 2 , 0 , 0 , 7 ) and Lambda ( 2 , 5 , 5 , 2 ) That's Mu ( 3 , 4 , 5 , 6 ) and Lambda ( 7 , 12 , 12 , 7 ) in Root notation. l(Lambda) = 9; l(Mu) = 4 P(Mu,Lambda) = ( +1 t^0 +2 t^2 ) Weyl(Mu, Lambda) = 186 Rank = 68 For Mu ( 7 , 1 , 0 , 4 ) and Lambda ( 2 , 5 , 5 , 2 ) That's Mu ( 7 , 7 , 6 , 5 ) and Lambda ( 7 , 12 , 12 , 7 ) in Root notation. l(Lambda) = 9; l(Mu) = 6 P(Mu,Lambda) = ( +1 t^0 +1 t^2 ) Weyl(Mu, Lambda) = 30 Rank = 16 For Mu ( 0 , 7 , 2 , 0 ) and Lambda ( 2 , 5 , 5 , 2 ) That's Mu ( 5 , 10 , 8 , 4 ) and Lambda ( 7 , 12 , 12 , 7 ) in Root notation. l(Lambda) = 9; l(Mu) = 6 P(Mu,Lambda) = ( +1 t^0 +1 t^2 ) Weyl(Mu, Lambda) = 57 Rank = 24 For Mu ( 4 , 0 , 1 , 7 ) and Lambda ( 2 , 5 , 5 , 2 ) That's Mu ( 5 , 6 , 7 , 7 ) and Lambda ( 7 , 12 , 12 , 7 ) in Root notation. l(Lambda) = 9; l(Mu) = 6 P(Mu,Lambda) = ( +1 t^0 +1 t^2 ) Weyl(Mu, Lambda) = 30 Rank = 16 For Mu ( 0 , 2 , 7 , 0 ) and Lambda ( 2 , 5 , 5 , 2 ) That's Mu ( 4 , 8 , 10 , 5 ) and Lambda ( 7 , 12 , 12 , 7 ) in Root notation. l(Lambda) = 9; l(Mu) = 6 P(Mu,Lambda) = ( +1 t^0 +1 t^2 ) Weyl(Mu, Lambda) = 57 Rank = 24 For Mu ( 5 , 1 , 0 , 7 ) and Lambda ( 2 , 5 , 5 , 2 ) That's Mu ( 6 , 7 , 7 , 7 ) and Lambda ( 7 , 12 , 12 , 7 ) in Root notation. l(Lambda) = 9; l(Mu) = 7 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 16 Rank = 11 For Mu ( 7 , 0 , 1 , 5 ) and Lambda ( 2 , 5 , 5 , 2 ) That's Mu ( 7 , 7 , 7 , 6 ) and Lambda ( 7 , 12 , 12 , 7 ) in Root notation. l(Lambda) = 9; l(Mu) = 7 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 16 Rank = 11 For Mu ( 1 , 7 , 2 , 1 ) and Lambda ( 2 , 5 , 5 , 2 ) That's Mu ( 6 , 11 , 9 , 5 ) and Lambda ( 7 , 12 , 12 , 7 ) in Root notation. l(Lambda) = 9; l(Mu) = 7 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 16 Rank = 9 For Mu ( 1 , 2 , 7 , 1 ) and Lambda ( 2 , 5 , 5 , 2 ) That's Mu ( 5 , 9 , 11 , 6 ) and Lambda ( 7 , 12 , 12 , 7 ) in Root notation. l(Lambda) = 9; l(Mu) = 7 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 16 Rank = 9 For Mu ( 2 , 7 , 3 , 0 ) and Lambda ( 2 , 5 , 5 , 2 ) That's Mu ( 7 , 12 , 10 , 5 ) and Lambda ( 7 , 12 , 12 , 7 ) in Root notation. l(Lambda) = 9; l(Mu) = 8 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 3 Rank = 2 For Mu ( 0 , 3 , 7 , 2 ) and Lambda ( 2 , 5 , 5 , 2 ) That's Mu ( 5 , 10 , 12 , 7 ) and Lambda ( 7 , 12 , 12 , 7 ) in Root notation. l(Lambda) = 9; l(Mu) = 8 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 3 Rank = 2 For Mu ( 0 , 7 , 3 , 3 ) and Lambda ( 2 , 5 , 5 , 2 ) That's Mu ( 6 , 12 , 11 , 7 ) and Lambda ( 7 , 12 , 12 , 7 ) in Root notation. l(Lambda) = 9; l(Mu) = 9 P(Mu,Lambda) = ( ) Weyl(Mu, Lambda) = 1 Rank = 1 For Mu ( 3 , 3 , 7 , 0 ) and Lambda ( 2 , 5 , 5 , 2 ) That's Mu ( 7 , 11 , 12 , 6 ) and Lambda ( 7 , 12 , 12 , 7 ) in Root notation. l(Lambda) = 9; l(Mu) = 9 P(Mu,Lambda) = ( ) Weyl(Mu, Lambda) = 1 Rank = 1 For Mu ( 8 , 0 , 0 , 3 ) and Lambda ( 2 , 5 , 5 , 2 ) That's Mu ( 7 , 6 , 5 , 4 ) and Lambda ( 7 , 12 , 12 , 7 ) in Root notation. l(Lambda) = 9; l(Mu) = 5 P(Mu,Lambda) = ( +1 t^0 +2 t^2 ) Weyl(Mu, Lambda) = 42 Rank = 21 For Mu ( 3 , 0 , 0 , 8 ) and Lambda ( 2 , 5 , 5 , 2 ) That's Mu ( 4 , 5 , 6 , 7 ) and Lambda ( 7 , 12 , 12 , 7 ) in Root notation. l(Lambda) = 9; l(Mu) = 5 P(Mu,Lambda) = ( +1 t^0 +2 t^2 ) Weyl(Mu, Lambda) = 42 Rank = 21 For Mu ( 7 , 0 , 0 , 7 ) and Lambda ( 2 , 5 , 5 , 2 ) That's Mu ( 7 , 7 , 7 , 7 ) and Lambda ( 7 , 12 , 12 , 7 ) in Root notation. l(Lambda) = 9; l(Mu) = 8 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 6 Rank = 5 For Mu ( 0 , 8 , 2 , 2 ) and Lambda ( 2 , 5 , 5 , 2 ) That's Mu ( 6 , 12 , 10 , 6 ) and Lambda ( 7 , 12 , 12 , 7 ) in Root notation. l(Lambda) = 9; l(Mu) = 8 P(Mu,Lambda) = ( ) Weyl(Mu, Lambda) = 2 Rank = 2 For Mu ( 2 , 2 , 8 , 0 ) and Lambda ( 2 , 5 , 5 , 2 ) That's Mu ( 6 , 10 , 12 , 6 ) and Lambda ( 7 , 12 , 12 , 7 ) in Root notation. l(Lambda) = 9; l(Mu) = 8 P(Mu,Lambda) = ( ) Weyl(Mu, Lambda) = 2 Rank = 2 For Mu ( 0 , 0 , 0 , 0 ) and Lambda ( 5 , 5 , 5 , 5 ) That's Mu ( 0 , 0 , 0 , 0 ) and Lambda ( 10 , 15 , 15 , 10 ) in Root notation. l(Lambda) = 10; l(Mu) = 0 P(Mu,Lambda) = ( +1 t^0 +5 t^2 +7 t^4 +6 t^6 +2 t^8 ) Weyl(Mu, Lambda) = 12216 Rank = 9875 For Mu ( 3 , 0 , 0 , 3 ) and Lambda ( 5 , 5 , 5 , 5 ) That's Mu ( 3 , 3 , 3 , 3 ) and Lambda ( 10 , 15 , 15 , 10 ) in Root notation. l(Lambda) = 10; l(Mu) = 1 P(Mu,Lambda) = ( +1 t^0 +5 t^2 +7 t^4 +6 t^6 +2 t^8 ) Weyl(Mu, Lambda) = 7608 Rank = 6398 For Mu ( 4 , 0 , 1 , 2 ) and Lambda ( 5 , 5 , 5 , 5 ) That's Mu ( 4 , 4 , 4 , 3 ) and Lambda ( 10 , 15 , 15 , 10 ) in Root notation. l(Lambda) = 10; l(Mu) = 2 P(Mu,Lambda) = ( +1 t^0 +5 t^2 +5 t^4 +2 t^6 ) Weyl(Mu, Lambda) = 6118 Rank = 5221 For Mu ( 2 , 1 , 0 , 4 ) and Lambda ( 5 , 5 , 5 , 5 ) That's Mu ( 3 , 4 , 4 , 4 ) and Lambda ( 10 , 15 , 15 , 10 ) in Root notation. l(Lambda) = 10; l(Mu) = 2 P(Mu,Lambda) = ( +1 t^0 +5 t^2 +5 t^4 +2 t^6 ) Weyl(Mu, Lambda) = 6118 Rank = 5221 For Mu ( 5 , 1 , 0 , 2 ) and Lambda ( 5 , 5 , 5 , 5 ) That's Mu ( 5 , 5 , 4 , 3 ) and Lambda ( 10 , 15 , 15 , 10 ) in Root notation. l(Lambda) = 10; l(Mu) = 3 P(Mu,Lambda) = ( +1 t^0 +4 t^2 +3 t^4 +1 t^6 ) Weyl(Mu, Lambda) = 4584 Rank = 3983 For Mu ( 3 , 1 , 1 , 3 ) and Lambda ( 5 , 5 , 5 , 5 ) That's Mu ( 4 , 5 , 5 , 4 ) and Lambda ( 10 , 15 , 15 , 10 ) in Root notation. l(Lambda) = 10; l(Mu) = 3 P(Mu,Lambda) = ( +1 t^0 +5 t^2 +3 t^4 ) Weyl(Mu, Lambda) = 4910 Rank = 4259 For Mu ( 2 , 0 , 1 , 5 ) and Lambda ( 5 , 5 , 5 , 5 ) That's Mu ( 3 , 4 , 5 , 5 ) and Lambda ( 10 , 15 , 15 , 10 ) in Root notation. l(Lambda) = 10; l(Mu) = 3 P(Mu,Lambda) = ( +1 t^0 +4 t^2 +3 t^4 +1 t^6 ) Weyl(Mu, Lambda) = 4584 Rank = 3983 For Mu ( 4 , 2 , 0 , 3 ) and Lambda ( 5 , 5 , 5 , 5 ) That's Mu ( 5 , 6 , 5 , 4 ) and Lambda ( 10 , 15 , 15 , 10 ) in Root notation. l(Lambda) = 10; l(Mu) = 4 P(Mu,Lambda) = ( +1 t^0 +4 t^2 +1 t^4 ) Weyl(Mu, Lambda) = 3666 Rank = 3246 For Mu ( 3 , 0 , 2 , 4 ) and Lambda ( 5 , 5 , 5 , 5 ) That's Mu ( 4 , 5 , 6 , 5 ) and Lambda ( 10 , 15 , 15 , 10 ) in Root notation. l(Lambda) = 10; l(Mu) = 4 P(Mu,Lambda) = ( +1 t^0 +4 t^2 +1 t^4 ) Weyl(Mu, Lambda) = 3666 Rank = 3246 For Mu ( 0 , 4 , 4 , 0 ) and Lambda ( 5 , 5 , 5 , 5 ) That's Mu ( 4 , 8 , 8 , 4 ) and Lambda ( 10 , 15 , 15 , 10 ) in Root notation. l(Lambda) = 10; l(Mu) = 4 P(Mu,Lambda) = ( +1 t^0 +5 t^2 +3 t^4 ) Weyl(Mu, Lambda) = 2120 Rank = 1921 For Mu ( 5 , 2 , 0 , 4 ) and Lambda ( 5 , 5 , 5 , 5 ) That's Mu ( 6 , 7 , 6 , 5 ) and Lambda ( 10 , 15 , 15 , 10 ) in Root notation. l(Lambda) = 10; l(Mu) = 5 P(Mu,Lambda) = ( +1 t^0 +2 t^2 ) Weyl(Mu, Lambda) = 1988 Rank = 1836 For Mu ( 1 , 5 , 3 , 0 ) and Lambda ( 5 , 5 , 5 , 5 ) That's Mu ( 5 , 9 , 8 , 4 ) and Lambda ( 10 , 15 , 15 , 10 ) in Root notation. l(Lambda) = 10; l(Mu) = 5 P(Mu,Lambda) = ( +1 t^0 +4 t^2 +1 t^4 ) Weyl(Mu, Lambda) = 1542 Rank = 1419 For Mu ( 4 , 0 , 2 , 5 ) and Lambda ( 5 , 5 , 5 , 5 ) That's Mu ( 5 , 6 , 7 , 6 ) and Lambda ( 10 , 15 , 15 , 10 ) in Root notation. l(Lambda) = 10; l(Mu) = 5 P(Mu,Lambda) = ( +1 t^0 +2 t^2 ) Weyl(Mu, Lambda) = 1988 Rank = 1836 For Mu ( 0 , 3 , 5 , 1 ) and Lambda ( 5 , 5 , 5 , 5 ) That's Mu ( 4 , 8 , 9 , 5 ) and Lambda ( 10 , 15 , 15 , 10 ) in Root notation. l(Lambda) = 10; l(Mu) = 5 P(Mu,Lambda) = ( +1 t^0 +4 t^2 +1 t^4 ) Weyl(Mu, Lambda) = 1542 Rank = 1419 For Mu ( 5 , 1 , 1 , 5 ) and Lambda ( 5 , 5 , 5 , 5 ) That's Mu ( 6 , 7 , 7 , 6 ) and Lambda ( 10 , 15 , 15 , 10 ) in Root notation. l(Lambda) = 10; l(Mu) = 6 P(Mu,Lambda) = ( +1 t^0 +1 t^2 ) Weyl(Mu, Lambda) = 1449 Rank = 1370 For Mu ( 2 , 5 , 3 , 1 ) and Lambda ( 5 , 5 , 5 , 5 ) That's Mu ( 6 , 10 , 9 , 5 ) and Lambda ( 10 , 15 , 15 , 10 ) in Root notation. l(Lambda) = 10; l(Mu) = 6 P(Mu,Lambda) = ( +1 t^0 +2 t^2 ) Weyl(Mu, Lambda) = 792 Rank = 753 For Mu ( 1 , 3 , 5 , 2 ) and Lambda ( 5 , 5 , 5 , 5 ) That's Mu ( 5 , 9 , 10 , 6 ) and Lambda ( 10 , 15 , 15 , 10 ) in Root notation. l(Lambda) = 10; l(Mu) = 6 P(Mu,Lambda) = ( +1 t^0 +2 t^2 ) Weyl(Mu, Lambda) = 792 Rank = 753 For Mu ( 2 , 4 , 4 , 2 ) and Lambda ( 5 , 5 , 5 , 5 ) That's Mu ( 6 , 10 , 10 , 6 ) and Lambda ( 10 , 15 , 15 , 10 ) in Root notation. l(Lambda) = 10; l(Mu) = 7 P(Mu,Lambda) = ( +1 t^0 +1 t^2 ) Weyl(Mu, Lambda) = 566 Rank = 547 For Mu ( 3 , 5 , 4 , 0 ) and Lambda ( 5 , 5 , 5 , 5 ) That's Mu ( 7 , 11 , 10 , 5 ) and Lambda ( 10 , 15 , 15 , 10 ) in Root notation. l(Lambda) = 10; l(Mu) = 7 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 370 Rank = 360 For Mu ( 0 , 4 , 5 , 3 ) and Lambda ( 5 , 5 , 5 , 5 ) That's Mu ( 5 , 10 , 11 , 7 ) and Lambda ( 10 , 15 , 15 , 10 ) in Root notation. l(Lambda) = 10; l(Mu) = 7 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 370 Rank = 360 For Mu ( 1 , 5 , 4 , 3 ) and Lambda ( 5 , 5 , 5 , 5 ) That's Mu ( 6 , 11 , 11 , 7 ) and Lambda ( 10 , 15 , 15 , 10 ) in Root notation. l(Lambda) = 10; l(Mu) = 8 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 259 Rank = 255 For Mu ( 3 , 4 , 5 , 1 ) and Lambda ( 5 , 5 , 5 , 5 ) That's Mu ( 7 , 11 , 11 , 6 ) and Lambda ( 10 , 15 , 15 , 10 ) in Root notation. l(Lambda) = 10; l(Mu) = 8 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 259 Rank = 255 For Mu ( 2 , 5 , 5 , 2 ) and Lambda ( 5 , 5 , 5 , 5 ) That's Mu ( 7 , 12 , 12 , 7 ) and Lambda ( 10 , 15 , 15 , 10 ) in Root notation. l(Lambda) = 10; l(Mu) = 9 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 112 Rank = 111 For Mu ( 5 , 5 , 5 , 5 ) and Lambda ( 5 , 5 , 5 , 5 ) That's Mu ( 10 , 15 , 15 , 10 ) and Lambda ( 10 , 15 , 15 , 10 ) in Root notation. l(Lambda) = 10; l(Mu) = 10 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 1 Rank = 1 For Mu ( 7 , 0 , 0 , 2 ) and Lambda ( 5 , 5 , 5 , 5 ) That's Mu ( 6 , 5 , 4 , 3 ) and Lambda ( 10 , 15 , 15 , 10 ) in Root notation. l(Lambda) = 10; l(Mu) = 4 P(Mu,Lambda) = ( +1 t^0 +3 t^2 +2 t^4 ) Weyl(Mu, Lambda) = 3156 Rank = 2806 For Mu ( 2 , 0 , 0 , 7 ) and Lambda ( 5 , 5 , 5 , 5 ) That's Mu ( 3 , 4 , 5 , 6 ) and Lambda ( 10 , 15 , 15 , 10 ) in Root notation. l(Lambda) = 10; l(Mu) = 4 P(Mu,Lambda) = ( +1 t^0 +3 t^2 +2 t^4 ) Weyl(Mu, Lambda) = 3156 Rank = 2806 For Mu ( 7 , 1 , 0 , 4 ) and Lambda ( 5 , 5 , 5 , 5 ) That's Mu ( 7 , 7 , 6 , 5 ) and Lambda ( 10 , 15 , 15 , 10 ) in Root notation. l(Lambda) = 10; l(Mu) = 6 P(Mu,Lambda) = ( +1 t^0 +1 t^2 ) Weyl(Mu, Lambda) = 1344 Rank = 1256 For Mu ( 0 , 7 , 2 , 0 ) and Lambda ( 5 , 5 , 5 , 5 ) That's Mu ( 5 , 10 , 8 , 4 ) and Lambda ( 10 , 15 , 15 , 10 ) in Root notation. l(Lambda) = 10; l(Mu) = 6 P(Mu,Lambda) = ( +1 t^0 +2 t^2 ) Weyl(Mu, Lambda) = 1032 Rank = 964 For Mu ( 4 , 0 , 1 , 7 ) and Lambda ( 5 , 5 , 5 , 5 ) That's Mu ( 5 , 6 , 7 , 7 ) and Lambda ( 10 , 15 , 15 , 10 ) in Root notation. l(Lambda) = 10; l(Mu) = 6 P(Mu,Lambda) = ( +1 t^0 +1 t^2 ) Weyl(Mu, Lambda) = 1344 Rank = 1256 For Mu ( 0 , 2 , 7 , 0 ) and Lambda ( 5 , 5 , 5 , 5 ) That's Mu ( 4 , 8 , 10 , 5 ) and Lambda ( 10 , 15 , 15 , 10 ) in Root notation. l(Lambda) = 10; l(Mu) = 6 P(Mu,Lambda) = ( +1 t^0 +2 t^2 ) Weyl(Mu, Lambda) = 1032 Rank = 964 For Mu ( 5 , 1 , 0 , 7 ) and Lambda ( 5 , 5 , 5 , 5 ) That's Mu ( 6 , 7 , 7 , 7 ) and Lambda ( 10 , 15 , 15 , 10 ) in Root notation. l(Lambda) = 10; l(Mu) = 7 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 980 Rank = 939 For Mu ( 7 , 0 , 1 , 5 ) and Lambda ( 5 , 5 , 5 , 5 ) That's Mu ( 7 , 7 , 7 , 6 ) and Lambda ( 10 , 15 , 15 , 10 ) in Root notation. l(Lambda) = 10; l(Mu) = 7 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 980 Rank = 939 For Mu ( 1 , 7 , 2 , 1 ) and Lambda ( 5 , 5 , 5 , 5 ) That's Mu ( 6 , 11 , 9 , 5 ) and Lambda ( 10 , 15 , 15 , 10 ) in Root notation. l(Lambda) = 10; l(Mu) = 7 P(Mu,Lambda) = ( +1 t^0 +1 t^2 ) Weyl(Mu, Lambda) = 506 Rank = 485 For Mu ( 1 , 2 , 7 , 1 ) and Lambda ( 5 , 5 , 5 , 5 ) That's Mu ( 5 , 9 , 11 , 6 ) and Lambda ( 10 , 15 , 15 , 10 ) in Root notation. l(Lambda) = 10; l(Mu) = 7 P(Mu,Lambda) = ( +1 t^0 +1 t^2 ) Weyl(Mu, Lambda) = 506 Rank = 485 For Mu ( 2 , 7 , 3 , 0 ) and Lambda ( 5 , 5 , 5 , 5 ) That's Mu ( 7 , 12 , 10 , 5 ) and Lambda ( 10 , 15 , 15 , 10 ) in Root notation. l(Lambda) = 10; l(Mu) = 8 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 224 Rank = 218 For Mu ( 9 , 2 , 4 , 0 ) and Lambda ( 5 , 5 , 5 , 5 ) That's Mu ( 10 , 11 , 10 , 5 ) and Lambda ( 10 , 15 , 15 , 10 ) in Root notation. l(Lambda) = 10; l(Mu) = 8 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 50 Rank = 48 For Mu ( 0 , 3 , 7 , 2 ) and Lambda ( 5 , 5 , 5 , 5 ) That's Mu ( 5 , 10 , 12 , 7 ) and Lambda ( 10 , 15 , 15 , 10 ) in Root notation. l(Lambda) = 10; l(Mu) = 8 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 224 Rank = 218 For Mu ( 0 , 4 , 2 , 9 ) and Lambda ( 5 , 5 , 5 , 5 ) That's Mu ( 5 , 10 , 11 , 10 ) and Lambda ( 10 , 15 , 15 , 10 ) in Root notation. l(Lambda) = 10; l(Mu) = 8 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 50 Rank = 48 For Mu ( 0 , 7 , 3 , 3 ) and Lambda ( 5 , 5 , 5 , 5 ) That's Mu ( 6 , 12 , 11 , 7 ) and Lambda ( 10 , 15 , 15 , 10 ) in Root notation. l(Lambda) = 10; l(Mu) = 9 P(Mu,Lambda) = ( ) Weyl(Mu, Lambda) = 148 Rank = 147 For Mu ( 1 , 5 , 1 , 9 ) and Lambda ( 5 , 5 , 5 , 5 ) That's Mu ( 6 , 11 , 11 , 10 ) and Lambda ( 10 , 15 , 15 , 10 ) in Root notation. l(Lambda) = 10; l(Mu) = 9 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 35 Rank = 34 For Mu ( 3 , 3 , 7 , 0 ) and Lambda ( 5 , 5 , 5 , 5 ) That's Mu ( 7 , 11 , 12 , 6 ) and Lambda ( 10 , 15 , 15 , 10 ) in Root notation. l(Lambda) = 10; l(Mu) = 9 P(Mu,Lambda) = ( ) Weyl(Mu, Lambda) = 148 Rank = 147 For Mu ( 9 , 1 , 5 , 1 ) and Lambda ( 5 , 5 , 5 , 5 ) That's Mu ( 10 , 11 , 11 , 6 ) and Lambda ( 10 , 15 , 15 , 10 ) in Root notation. l(Lambda) = 10; l(Mu) = 9 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 35 Rank = 34 For Mu ( 1 , 7 , 4 , 2 ) and Lambda ( 5 , 5 , 5 , 5 ) That's Mu ( 7 , 13 , 12 , 7 ) and Lambda ( 10 , 15 , 15 , 10 ) in Root notation. l(Lambda) = 10; l(Mu) = 10 P(Mu,Lambda) = ( ) Weyl(Mu, Lambda) = 56 Rank = 56 For Mu ( 2 , 4 , 7 , 1 ) and Lambda ( 5 , 5 , 5 , 5 ) That's Mu ( 7 , 12 , 13 , 7 ) and Lambda ( 10 , 15 , 15 , 10 ) in Root notation. l(Lambda) = 10; l(Mu) = 10 P(Mu,Lambda) = ( ) Weyl(Mu, Lambda) = 56 Rank = 56 For Mu ( 8 , 0 , 0 , 3 ) and Lambda ( 5 , 5 , 5 , 5 ) That's Mu ( 7 , 6 , 5 , 4 ) and Lambda ( 10 , 15 , 15 , 10 ) in Root notation. l(Lambda) = 10; l(Mu) = 5 P(Mu,Lambda) = ( +1 t^0 +2 t^2 ) Weyl(Mu, Lambda) = 1698 Rank = 1556 For Mu ( 3 , 0 , 0 , 8 ) and Lambda ( 5 , 5 , 5 , 5 ) That's Mu ( 4 , 5 , 6 , 7 ) and Lambda ( 10 , 15 , 15 , 10 ) in Root notation. l(Lambda) = 10; l(Mu) = 5 P(Mu,Lambda) = ( +1 t^0 +2 t^2 ) Weyl(Mu, Lambda) = 1698 Rank = 1556 For Mu ( 10 , 1 , 3 , 1 ) and Lambda ( 5 , 5 , 5 , 5 ) That's Mu ( 10 , 10 , 9 , 5 ) and Lambda ( 10 , 15 , 15 , 10 ) in Root notation. l(Lambda) = 10; l(Mu) = 7 P(Mu,Lambda) = ( +1 t^0 +1 t^2 ) Weyl(Mu, Lambda) = 70 Rank = 65 For Mu ( 1 , 3 , 1 , 10 ) and Lambda ( 5 , 5 , 5 , 5 ) That's Mu ( 5 , 9 , 10 , 10 ) and Lambda ( 10 , 15 , 15 , 10 ) in Root notation. l(Lambda) = 10; l(Mu) = 7 P(Mu,Lambda) = ( +1 t^0 +1 t^2 ) Weyl(Mu, Lambda) = 70 Rank = 65 For Mu ( 7 , 0 , 0 , 7 ) and Lambda ( 5 , 5 , 5 , 5 ) That's Mu ( 7 , 7 , 7 , 7 ) and Lambda ( 10 , 15 , 15 , 10 ) in Root notation. l(Lambda) = 10; l(Mu) = 8 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 666 Rank = 641 For Mu ( 2 , 4 , 0 , 10 ) and Lambda ( 5 , 5 , 5 , 5 ) That's Mu ( 6 , 10 , 10 , 10 ) and Lambda ( 10 , 15 , 15 , 10 ) in Root notation. l(Lambda) = 10; l(Mu) = 8 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 50 Rank = 48 For Mu ( 10 , 0 , 4 , 2 ) and Lambda ( 5 , 5 , 5 , 5 ) That's Mu ( 10 , 10 , 10 , 6 ) and Lambda ( 10 , 15 , 15 , 10 ) in Root notation. l(Lambda) = 10; l(Mu) = 8 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 50 Rank = 48 For Mu ( 0 , 8 , 2 , 2 ) and Lambda ( 5 , 5 , 5 , 5 ) That's Mu ( 6 , 12 , 10 , 6 ) and Lambda ( 10 , 15 , 15 , 10 ) in Root notation. l(Lambda) = 10; l(Mu) = 8 P(Mu,Lambda) = ( ) Weyl(Mu, Lambda) = 204 Rank = 202 For Mu ( 2 , 2 , 8 , 0 ) and Lambda ( 5 , 5 , 5 , 5 ) That's Mu ( 6 , 10 , 12 , 6 ) and Lambda ( 10 , 15 , 15 , 10 ) in Root notation. l(Lambda) = 10; l(Mu) = 8 P(Mu,Lambda) = ( ) Weyl(Mu, Lambda) = 204 Rank = 202 For Mu ( 1 , 8 , 3 , 1 ) and Lambda ( 5 , 5 , 5 , 5 ) That's Mu ( 7 , 13 , 11 , 6 ) and Lambda ( 10 , 15 , 15 , 10 ) in Root notation. l(Lambda) = 10; l(Mu) = 9 P(Mu,Lambda) = ( ) Weyl(Mu, Lambda) = 77 Rank = 77 For Mu ( 5 , 10 , 0 , 0 ) and Lambda ( 5 , 5 , 5 , 5 ) That's Mu ( 10 , 15 , 10 , 5 ) and Lambda ( 10 , 15 , 15 , 10 ) in Root notation. l(Lambda) = 10; l(Mu) = 9 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 6 Rank = 5 For Mu ( 1 , 3 , 8 , 1 ) and Lambda ( 5 , 5 , 5 , 5 ) That's Mu ( 6 , 11 , 13 , 7 ) and Lambda ( 10 , 15 , 15 , 10 ) in Root notation. l(Lambda) = 10; l(Mu) = 9 P(Mu,Lambda) = ( ) Weyl(Mu, Lambda) = 77 Rank = 77 For Mu ( 0 , 0 , 10 , 5 ) and Lambda ( 5 , 5 , 5 , 5 ) That's Mu ( 5 , 10 , 15 , 10 ) and Lambda ( 10 , 15 , 15 , 10 ) in Root notation. l(Lambda) = 10; l(Mu) = 9 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 6 Rank = 5 For Mu ( 0 , 7 , 0 , 9 ) and Lambda ( 5 , 5 , 5 , 5 ) That's Mu ( 6 , 12 , 11 , 10 ) and Lambda ( 10 , 15 , 15 , 10 ) in Root notation. l(Lambda) = 10; l(Mu) = 10 P(Mu,Lambda) = ( ) Weyl(Mu, Lambda) = 20 Rank = 20 For Mu ( 9 , 0 , 7 , 0 ) and Lambda ( 5 , 5 , 5 , 5 ) That's Mu ( 10 , 11 , 12 , 6 ) and Lambda ( 10 , 15 , 15 , 10 ) in Root notation. l(Lambda) = 10; l(Mu) = 10 P(Mu,Lambda) = ( ) Weyl(Mu, Lambda) = 20 Rank = 20 For Mu ( 0 , 8 , 5 , 1 ) and Lambda ( 5 , 5 , 5 , 5 ) That's Mu ( 7 , 14 , 13 , 7 ) and Lambda ( 10 , 15 , 15 , 10 ) in Root notation. l(Lambda) = 10; l(Mu) = 11 P(Mu,Lambda) = ( ) Weyl(Mu, Lambda) = 14 Rank = 14 For Mu ( 1 , 5 , 8 , 0 ) and Lambda ( 5 , 5 , 5 , 5 ) That's Mu ( 7 , 13 , 14 , 7 ) and Lambda ( 10 , 15 , 15 , 10 ) in Root notation. l(Lambda) = 10; l(Mu) = 11 P(Mu,Lambda) = ( ) Weyl(Mu, Lambda) = 14 Rank = 14 For Mu ( 11 , 0 , 3 , 0 ) and Lambda ( 5 , 5 , 5 , 5 ) That's Mu ( 10 , 9 , 8 , 4 ) and Lambda ( 10 , 15 , 15 , 10 ) in Root notation. l(Lambda) = 10; l(Mu) = 6 P(Mu,Lambda) = ( +1 t^0 +2 t^2 ) Weyl(Mu, Lambda) = 88 Rank = 81 For Mu ( 0 , 3 , 0 , 11 ) and Lambda ( 5 , 5 , 5 , 5 ) That's Mu ( 4 , 8 , 9 , 10 ) and Lambda ( 10 , 15 , 15 , 10 ) in Root notation. l(Lambda) = 10; l(Mu) = 6 P(Mu,Lambda) = ( +1 t^0 +2 t^2 ) Weyl(Mu, Lambda) = 88 Rank = 81 For Mu ( 10 , 0 , 0 , 10 ) and Lambda ( 5 , 5 , 5 , 5 ) That's Mu ( 10 , 10 , 10 , 10 ) and Lambda ( 10 , 15 , 15 , 10 ) in Root notation. l(Lambda) = 10; l(Mu) = 9 P(Mu,Lambda) = ( +1 t^0 ) Weyl(Mu, Lambda) = 6 Rank = 5 For Mu ( 0 , 9 , 4 , 0 ) and Lambda ( 5 , 5 , 5 , 5 ) That's Mu ( 7 , 14 , 12 , 6 ) and Lambda ( 10 , 15 , 15 , 10 ) in Root notation. l(Lambda) = 10; l(Mu) = 10 P(Mu,Lambda) = ( ) Weyl(Mu, Lambda) = 20 Rank = 20 For Mu ( 0 , 4 , 9 , 0 ) and Lambda ( 5 , 5 , 5 , 5 ) That's Mu ( 6 , 12 , 14 , 7 ) and Lambda ( 10 , 15 , 15 , 10 ) in Root notation. l(Lambda) = 10; l(Mu) = 10 P(Mu,Lambda) = ( ) Weyl(Mu, Lambda) = 20 Rank = 20