Ariki-Koike algebras with semisimple bottoms

Simple modules of Ariki{Koike algebras

Generic Degrees of Ariki–koike Algebras

This note describes how to compute the generic degrees of the Ariki–Koike algebras by first constructing a basis of matrix units inside the algebras. As a consequence, we are able to define an explicit isomorphism from any semisimple Ariki–Koike algebra to the group algebra of the corresponding complex reflection group. This article is based fairly closely on the talk that I gave in Osaka at th...

Morita equivalences of Ariki–Koike algebras

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...

Core blocks of Ariki–Koike algebras

We examine blocks of the Ariki–Koike algebra, in an attempt to generalise the combinatorial representation theory of the Iwahori–Hecke algebra of type A. We identify a particular type of combinatorial block, which we call a core block, which may be viewed as an analogue of a simple block of the Iwahori–Hecke algebra. We give equivalent characterisations of core blocks and examine their basic co...

Canonical bases and the decomposition matrices of Ariki–Koike algebras

In this paper we use a deep result of Ariki’s to give a combinatorial algorithm for computing the decomposition matrices of the Ariki–Koike algebras H over fields of characteristic zero. As a corollary we obtain a classification of the irreducible H – modules over an arbitrary field (for certain choices of the defining parameters). In this paper we describe how to explicitly compute the decompo...