On the action of Ariki–Koike algebras on tensor space

The action of the Ariki–Koike algebra on tensor space is used to show that the Ariki–Koike algebra is isomorphic to a direct sum of matrix rings over tensor products over smaller Ariki–Koike algebras. As an application we get Schur–Weyl duality for the action of the Ariki–Koike algebra and the Levi subalgebra of the q-Schur algebra when separation conditions holds.