#### Alladi Ramakrishnan Hall

#### Demazure flags: connections to algebraic combinatorics and number theory.

#### Rekha Biswal

##### Universite Laval, Canada

*In this talk, we will briefly review the basic theory of Demazure modules, which are modules over the standard maximal parabolic subalgebra of an affine Lie algebra. The discussion will be followed by a glimpse into some connections between the theory of Demazure flags, and algebraic combinatorics and number theory. For instance, we show that the graded multiplicities of higher level Demazure modules in Demazure flags can be expressed in terms of Dyck paths which are well-studied and ubiquitous combinatorial objects. The generating series for those graded multiplicities give rise to interesting connections with cone theta functions. We will also see the appearance of Pieri coefficients as multiplicities in Demazure flags in the case of \mathfrak{sl_n}[t]. I will describe some results and further questions in this direction.*

Done