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Demazure flags, q-Fibonacci polynomials and hypergeometric series

  • Rekha Biswal
  • Vyjayanthi Chari
  • Deniz Kus
Research
  • 71 Downloads

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.

Notes

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© SpringerNature 2018

Authors and Affiliations

  1. 1.The Institute of Mathematical SciencesChennaiIndia
  2. 2.Department of MathematicsUniversity of CaliforniaRiversideUSA
  3. 3.Mathematisches InstitutUniversität BonnBonnGermany

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