Rekha Biswal, Université Laval
"Demazure flags, Chebyshev polynomials and mock theta functions"
In this talk, we will explore some (surprising) connections between representation theory, combinatorics and number theory. We are interested in studying the Demazure modules in highest weight representations of affine Lie algebras. These modules are indexed by a pair consisting of a dominant integral weight of the underlying simple Lie algebra and a non-negative integer called the level. It is known that Demazure modules of fixed level \ell has a flag whose successive quotients are Demazure modules of level m for m \geq \ell. We shall see that the multiplicities in the flag give rise to interesting generating series which are connected in the case of sl_2 with Chebyshev polynomials and Ramanujan's fifth order mock theta functions and in higher rank to the cone theta functions.
MC 5403