A Brauer Algebra Theoretic Proof Of Littlewood's Restriction Rules

. Let U be a complex vector space endowed with an orthogonal or symplectic form, and let G be the subgroup of GL(U) of all the symmetries of this form (resp. O(U) or Sp(U)); if M is an irreducible GL(U)--module, the Littlewood's restriction rules describes the G--module M fi fi GL(U) G . In this paper we give a new representation-theoretic proof of this formula: realizing M in a tensor power U\Omega f and using Schur's duality we reduce to the problem of describing the restriction to an irreducible S f --module of an irreducible module for the centralizer algebra of the action of G on U\Omega f ; the latter is a quotient of the Brauer algebra, and we know the kernel of the natural epimorphism, whence we deduce the Littlewood's restriction rule. "Non potrai dir che quest' `e cosa dura: usando la dualit`a di Brauer dimostrazione dar, novella e pura" N. Barbecue, "Scholia" Introduction Let U be a complex vector space, endowed with an orthogonal or symplectic form, and let G be..