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- R. Dipper, Andrew Mathas
- 1998

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… (More)

- Andrew Mathas
- 1998

These notes give a fully self{contained introduction to the (modular) representation theory of the Iwahori{Hecke algebras and the q{Schur algebras of the symmetric groups. The central aim of this work is to give a concise, but complete, and an elegant, yet quick, treatment of the classiication of the simple modules and of the blocks of these two important… (More)

- Andrew Mathas
- 2007

In this paper we prove an analogue of Jantzen's sum formula for the q{Weyl modules of the q{Schur algebra and, as a consequence, derive the analogue of Schaper's theorem for the q{Specht modules of the Hecke algebras of type A. We apply these results to classify the irreducible q-Weyl modules and the irreducible (e{regular) q{Specht modules, deened over any… (More)

- Andrew Mathas
- 1998

In the representation theory of nite groups it is useful to know which ordinary irreducible representations remain irreducible modulo a prime p. For the symmetric groups S n this amounts to determining which Specht modules are irreducible over a eld of characteristic p. Throughout this note we work in characteristic 2, and in this case we classify the… (More)

- Andrew Mathas
- 2001

The cyclotomic Hecke algebras were introduced by Ariki and Koike [2,4] and Broué and Malle [7]. It is conjectured [7] that these algebras play a rôle in the representation theory of reductive groups similar to (but more complicated than) that played by the Iwahori–Hecke algebras (see, for example, [8]). In particular, it should be possible to use these… (More)

- Andrew Mathas
- 1996

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… (More)

In this note we classify the simple modules of the Ariki{Koike algebras when q = 1 and also describe the classiication for those algebras considered in 3, 14], together with the underlying computation of the computing canonical bases of an aane quantum group. In particular, this gives a classiication of the simple modules of the Iwahori{Hecke algebras of… (More)

In this paper we prove the Dipper–James conjecture that the centre of the Iwahori–Hecke algebra of type A is the set of symmetric polynomials in the Jucys–Murphy operators. © 2006 Elsevier Inc. All rights reserved.