Mathematics Colloquium 02-01-2001

Mathematics Colloquium

Thursday, February 1, at 4pm in 311 Cabell Hall
!! PLEASE NOTE CHANGED LOCATION !!

Gregory Landweber
(MSRI))

"Spin Representations and the Generalized Weyl Formula".

Abstract: Let G be a compact Lie group and T a maximal torus. The Weyl Character Formula expresses an irreducible representation V of G as the quotient of an alternating sum of one dimensional representations of T by the difference of the spin representation associated to G/T. Recently, Gross, Kostant, Ramond, and Sternberg noted a generalization which replaces T with a maximal rank reductive subgroup H containing T, associating to each irreducible representation V of G a set of H-representations called an Euler number multiplet. Furthermore, Kostant gave an explicit construction of such multiplets as the kernel of a formal Dirac operator on V-valued spinors. Conversely, given a representation U of H, the corresponding G-representation can be constructed as the index of the geometric Dirac operator on the homogeneous space G/H twisted by the bundle induced by U. This talk outlines the proof of these results and discusses their analogues in the Kac-Moody setting for homogeneous loop spaces.

Refreshments at 3:30 in 314 Kerchof Hall