Schur-Weyl reciprocity for Ariki-Koike algebras

Abstract

Let g=glm1⊕···⊕ glmr be a Levi subalgebra of glm, with m=∑ri=1mi, and V the natural representation of the quantum group Uq(g). We construct a representation of the Ariki-Koike algebra Hn,r on the n-fold tensor space of V, commuting with the action of Uq(g), and prove the Schur-Weyl reciprocity for the actions of Uq(g) and Hn,r on it. © 1999 Academic Press.