Representations of the Brauer Algebra and Littlewoodʹs Restriction Rules Original Research Article

LetGbe eitherSp(V) orO(V). Using an action of the Brauer algebra, we describe the subspaceTk(V circle times operator m) subset of or equal to V circle times operator mof tensors of valencekas an induced representation of the symmetric groupSm. As an application, we recover a special case of Littlewoodʹs restriction rule, affording the decomposition of an irreducibleGL(V)-module when restricted toG. Moreover we get an explicit realization of the irreducible representations of the Brauer algebra.