Morita equivalences of Ariki-Koike algebras

Richard Dipper and Andrew Mathas


Ariki-Koike algebras, Morita equivalences.


Math. Z., to appear.


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.

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Andrew Mathas
17th July 2001