Title:    Morita equivalences of Ariki-Koike algebras.
Authors:  Richard Dipper and Andrew Mathas.

Keywords: Ariki-Koike algebras, Morita equivalences. 

Status:   Submitted for publication.

Abstract:
We prove that every Ariki-Koike algebra is Morita equivalent to a
direct sum of tensor products of smaller Ariki-Koike algebras which
have $q$-connected parameter sets. A similar result is proved for
the cyclotomic $q$-Schur algebras. Combining our results with work
of Ariki and Uglov, the decomposition numbers for the Ariki-Koike
algebras defined over fields of characteristic zero are now known in
principle.