Morita equivalences of Ariki-Koike algebras

Details Morita equivalences of Ariki-Koike algebras Morita equivalences of Ariki-Koike algebras

2000-04-04

arxiv.org/abs/math/0004014v1

Mathematics

Representation Theory

LaTeX 2e file. 30 pages. Submitted for publication

Scientific paper

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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