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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Received: 22 March 2000; in final form: 19 September 2001 / Published online: 29 April 2002
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Dipper, R., Mathas, A. Morita equivalences of Ariki–Koike algebras. Math Z 240, 579–610 (2002). https://doi.org/10.1007/s002090100371
- Mathematics Subject Classification (1991): 20C08, 16G99, 20G05