An estimate of multiplicities in the branching rule for a Levi subgroup

Abstract

Let G be a connected reductive linear algebraic group defined over an algebraically closed field of zero characteristic, V λ a simple G-module with highest weight λ, P a parabolic subgroup of G, and L a Levi subgroup of P. Generalizing a result of M. Demazure, we give an upper bound for the multiplicities of simple L-modules in the decomposition of the restricted G-module res L V λ. From this we get information about the rate of decay of relative multiplicities for certain simple subgroups of simple groups.