This course provides the opportunity to offer a new topic in the subject of mathematics.

Seminars

no topology seminar

Daniel Orr (Virginia Tech) - Generalized Weyl modules and nonsymmetric q-Whittaker functions

Generalized Weyl modules and nonsymmetric q-Whittaker functions

The current algebra of a finite-dimensional simple Lie algebra has a family of universal highest weight modules known as Weyl modules. It turns out that the graded characters of Weyl modules can be expressed in terms of some well-known objects from algebraic combinatorics, namely: Macdonald polynomials specialized at t=0. Studying all of these graded characters simultaneously (e.g., in a generating function) produces an eigenfunction of the q-Toda system of difference operators (a q-Whittaker function). All this has been studied from several points of view (algebraic and geometric) by Chari-Ion, Cherednik, Braverman-Finkelberg, and others. This talk will focus on a "nonsymmetric" generalization of these results, obtained in joint work with Evgeny Feigin and Ievgen Makedonskyi, to a class of modules for the Iwahori subalgebra of the current algebra.

Daniel OrrGeneralized Weyl modules and nonsymmetric q-Whittaker functions

The current algebra of a finite-dimensional simple Lie algebra has a family of universal highest weight modules known as Weyl modules. It turns out that the graded characters of Weyl modules can be expressed in terms of some well-known objects from algebraic combinatorics, namely: Macdonald polynomials specialized at t=0. Studying all of these graded characters simultaneously (e.g., in a generating function) produces an eigenfunction of the q-Toda system of difference operators (a q-Whittaker function). All this has been studied from several points of view (algebraic and geometric) by Chari-Ion, Cherednik, Braverman-Finkelberg, and others. This talk will focus on a "nonsymmetric" generalization of these results, obtained in joint work with Evgeny Feigin and Ievgen Makedonskyi, to a class of modules for the Iwahori subalgebra of the current algebra.

" class="addtocalendar" target="_new">Add to Google CalendarLisa Piccirillo (UT Austin) - TBA

Harmonic analysis and PDE seminar (UVA)

UVA Math Club - Panel discussion on math classes enrollment

Lloyd West (UVA) - TBA

*A random selection of our faculty*

MATH 9559

This course provides the opportunity to offer a new topic in the subject of mathematics.