A Brauer Algebra Theoretic Proof of Littlewood's Restriction Rules

  • Fabio Gavarini
  • Published 1997

Abstract

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 GL(U) G. In this paper we give a new representation-theoretic proof of this formula: realizing M in a tensor power U 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 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 dualitt a di Brauer dimostrazione dar, novella e pura" N. Barbecue, "Scholia"

Cite this paper

@inproceedings{Gavarini1997ABA, title={A Brauer Algebra Theoretic Proof of Littlewood's Restriction Rules}, author={Fabio Gavarini}, year={1997} }