On Dipper–Mathas’s morita equivalences

Dipper and Mathas have proved that every Ariki–Koike algebra (i.e., nondegenerate cyclotomic Hecke algebra of type G(ℓ, 1, n)) is Morita equivalent to a direct sum of tensor products of some smaller Ariki–Koike algebras which have q-connected parameter sets. They proved this result by explicitly constructing a progenerator which induces this equivalence. In this paper we use the nondegenerate affine Hecke algebra H_n ^aff to derive Dipper–Mathas’s Morita equivalence as a consequence of an equivalence between the block H_n ^aff -mod[γ] of the category of finite-dimensional modules over H_n ^aff and the block H_n1 ^aff ⊗ · · · ⊗ H_nr ^aff -mod[(γ⁽¹⁾, …, γ^(r))] of the category of finite-dimensional modules over the parabolic subalgebra H_n1 ^aff ⊗ · · · ⊗ H_nr ^aff under certain conditions on γ, γ⁽¹⁾, …, γ^(r). Similar results for the degenerate versions of these algebras are also obtained.