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.