Seminars & Colloquia Calendar

 Abstract:   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 some connections that I have discovered (with collaborators) in my own research between algebraic combinatorics and other areas of mathematics such as representation theory 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. The generating series for those graded multiplicities give rise to interesting connections with Ramanujan's mock theta functions. I will describe some results and further questions in this direction.