Combinatorics Seminar: Macdonald polynomials and level two Demazure modules for affine $sl_{n+1}$.

Seminar | February 3 | 12:10-1 p.m. | 939 Evans Hall

 Rekha Biswal, MPIM Bonn

 Department of Mathematics

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.