Alladi Ramakrishnan Hall

Demazure flags, Chebyshev polynomials, Mock theta functions.

Rekha Biswal (PhD thesis defence)

IMSc

The g[t]-stable Demazure modules are of great 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 \geq \ell, D(\ell,
\lambda) admits a level m Demazure flag for an arbitrary simple Lie
algebra g. Chari et al. gave a direct and constructive proof of Naoi's
theorem in the case of sl_2. 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 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 relates to
Ramanujan's fifth order mock theta functions (surprisingly) in certain
special cases .