Representations of the Brauer algebra and Littlewood's restriction rules

Let G be either Sp(V) or O(V). Using an action of the Brauer algebra, we describe the subspace T^k(V^{\otimes m}) ⊆ V^{\otimes m} of tensors of valence k as an induced representation of the symmetric group S_m . 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.