Mathematics

Dr.Rekha Biswal
Max Planck Institute for Mathematics, Bonn

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.