Quantum affine algebras and affine Hecke algebras

Abstract

We describe a functor from the category Cm of finite-dimensional representations of the affine Hecke algebra of GL(m) to the category Dn of finite-dimensional representations of affine s/(n). If m < n, this functor is an equivalence between Cm and the subcategory of Dn consisting of those representations whose irreducible components under quantum sl(n) all occur in the m-fold tensor product of the natural representation of quantum sl(n). These results are analogous to the classical Frobenius-Schur duality between the representations of general linear and symmetric groups.