A Brauer algebra theoretic proof of Littlewood's restriction rules

Let U be a complex vector space endowed with an orthogonal or symplectic fo rm, and let G be the subgroup of GL(U) of all the symmetries of this form ( resp. O(Li) or Sp(U)); if M is an irreducible GL(U)-module, the Littlewood' s restriction rule describes the G-module M\(GL(U)(G)). In this paper we gi ve a new representation-theoretic proof of this formula: realizing iii in a tensor power U-xf and using Schur's duality, we reduce to the problem of d escribing the restriction to an irreducible S-f-module of an irreducible mo dule for the centralizer algebra of the action of G on U-xf: the latter is a quotient of the Brauer algebra, and we know the kernel of the natural epi morphism, whence we deduce the Littlewood's restriction rule. (C) 1999 Acad emic Press.