On Dipper-Mathas’ S Morita Equivalence

Dipper and Mathas have proved that every Ariki–Koike algebra is Morita equivalent to a direct sum of tensor products of some smaller Ariki–Koike algebras which have q–connected cyclotomic parameters. They proved this result by constructing explicitly the progenerator which induces this equivalence. In this paper we use the theory of affine Hecke algebra Haff nto rederive Dipper–Mathas’ s Morita equivalence as a consequence of an equivalence between the block Haff n-mod[γ(1)∪ · · · ∪ γ(r)] of the category of finite dimensional modules over the affine Hecke algebra Haff nand the block Haffμ-mod[(γ(1),..., γ(r))] of the category of finite dimensional modules over the parabolic subalgebra Haffμ, where μ is a composition of n.