Reduction rules for Demazure modules

Marc Besson, Sam Jeralds, Joshua Kiers

Abstract

For \(G\) a complex reductive group and \(B \subseteq G\) a Borel subgroup, we provide a reduction rule for certain weight multiplicities in Demazure modules \(V_\lambda^w\): given a weight \(\mu\) on a face of the associated weight polytope \(P_\lambda^w\), we reduce the computation of the dimension of the weight space \(V_\lambda^w(\mu)\) to a similar problem of computing the weight space dimension for a Demazure module of a Levi subgroup of \(G\).

Keywords: Schubert variety, Demazure, inequalities, polytope.

AMS Subject Classification: Primary 14M15; secondary 22E46, 17B10, 05E10, 52A40.