Andrew Mathas

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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)
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)
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)
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)
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)