Reduction rules for Demazure modules

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 $V_{\hat{I}}{»}^w$: given a weight $\hat{I}¼$ on a face of the associated weight polytope $P_{\hat{I}}{»}^w$, we reduce the computation of the dimension of the weight space $V_{\hat{I}}{»}^w(\hat{I}¼)$ to a similar problem of computing the weight space dimension for a Demazure module of a Levi subgroup of $G$.

18 pages, 3 figure