Demazure flags, q-Fibonacci polynomials and hypergeometric series

Abstract

We study a family of finite-dimensional representations of the hyperspecial parabolic subalgebra of the twisted affine Lie algebra of type $$\mathtt A_2^{(2)}$$ . We prove that these modules admit a decreasing filtration whose sections are isomorphic to stable Demazure modules in an integrable highest weight module of sufficiently large level. In particular, we show that any stable level $$m'$$ Demazure module admits a filtration by level m Demazure modules for all $$m\ge m'$$ . We define the graded and weighted generating functions which encode the multiplicity of a given Demazure module and establish a recursive formulae. In the case when $$m'=1,2$$ and $$m=2,3$$ , we determine these generating functions completely and show that they define hypergeometric series and that they are related to the q-Fibonacci polynomials defined by Carlitz.