Representations of the normalizers of maximal tori of simple Lie groups

Abstract

We study the branching rule for the restriction from a complex simple Lie group $G$ to the normalizer of a maximal torus of $G$. We show that the problem is reduced to the determination of the Weyl group module structures induced on the zero weight spaces of representations of semisimple Lie groups. The concrete formulas are obtained for $SL$($n$, C) in terms of generalized q-binomial coeffcients and Schur functions.