Description
CACAAG seminar.
Speaker: Rekha Biswal.
Affiliation: Max Planck Institute for Mathematics, Bonn, Germany.
Date and Time: Thursday 19 September, 4:00 pm - 5:00 pm.
Venue: Ramanujan Hall, Department of Mathematics.
Title: Macdonald polynomials and level two Demazure modules for affine
sl_{n+1}.
Abstract:- Macdonald polynomials are a remarkable family of orthogonal
symmetric polynomials in several variables. An enormous amount of
combinatorics, group theory, algebraic geometry and representation theory
is encoded in these polynomials. It is known that the characters of level
one Demazure modules are non-symmetric Macdonald polynomials specialized
at t=0. In this talk, I will define a class of polynomials in terms of
symmetric Macdonald polynomials and using representation theory we will
see that these polynomials are Schur-positive and are equal to the graded
character of level two Demazure modules for affine sl_{n+1}. As an
application we will see how this gives rise to an explicit formula for the
graded multiplicities of level two Demazure modules in the excellent
filtration of Weyl modules. This is based on joint work with Vyjayanthi
Chari, Peri Shereen and Jeffrey Wand.