Monday, June 5, 2017 at 2:00 PM in SAS 4201
Rekha Biswal, Universite Laval, Canada
Demazure flags, Chebyshev polynomials and mock theta functions
The g[t]-stable Demazure modules are a lot of interest because of their connections to representation theory of quantum affine algebras. These modules are indexed by a pair (ell, lambda) where ell is a positive integer and lambda is a dominant integral weight of g and are denoted as D(ell,lambda). Naoi proves that for m>=ell, D(ell,lambda) admits a level m Demazure flag for an arbitrary simple Lie algebra g. In this talk, we will discuss the level m Demazure flag of D(ell,lambda) for the current algebra associated to sl_2. We will give a direct and constructive proof of Naois theorem in the case of sl_2. We will also see how the generating series of numerical multiplicities of Demazure modules in the Demazure flag of local Weyl modules relates to Chebyshev polynomials and how the generating series of graded multiplicities of Demazure modules in local Weyl modules relate to Ramanujans fifth order mock theta functions (surprisingly) in certain special cases. This is based on joint work with Vyjayanthi Chari, Lisa Schneider and Sankaran Viswanath.
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