Representations of the Brauer algebra and Littlewood's restriction rules

Abstract

Let G be either Sp(V) or O(V). Using an action of the Brauer algebra, we describe the subspace Tk(V⊗m) ⊆ V⊗m of tensors of valence k as an induced representation of the symmetric group Sm. As an application, we recover a special case of Littlewood's restriction rule, affording the decomposition of an irreducible GL(V)-module when restricted to G. Moreover we get an explicit realization of the irreducible representations of the Brauer algebra. © 1997 Academic Press.