Rekha Biswal: Macdonald polynomials and level two Demazure modules for affine sl_{n+1}.
Abstract
An important result due to Sanderson and Ion says that
characters of level one Demazure modules are specialized Macdonald polynomials.
In this talk, I will introduce a new class of symmetric polynomials
indexed by a pair of dominant weights of sl_{n+1} which is expressed as linear
combination of specialized symmetric Macdonald polynomials with coefficients
defined recursively. These polynomials arose in my own work while investigating
the characters of higher level Demazure modules. Using representation theory
we will see that these new family of polynomials interpolate between characters of
level one and level two Demazure modules for affine sl_{n+1} and gives rise to
new results in the representation theory of current algebras as a corollary.