Schur–Weyl Reciprocity for Ariki–Koike Algebras,

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