The cyclotomic Jantzen-Schaper theorem

Gordon James and Andrew Mathas

Keywords

Ariki-Koike algebras, cyclotomic q-Schur algebras, Jantzen filtrations.

Status

Trans. AMS, 352 (2000), 5381-5404.
MR2001b:16017.

Abstract

In this paper we use the cyclotomic q-Schur algebras to prove an analogue of the Jantzen-Schaper theorem for the Ariki-Koike algebras. Most of the argument is devoted to first proving an analogue of Jantzen's sum formula for the Weyl modules of the cyclotomic q-Schur algebra. The result for the Ariki-Koike algebras is then deduced by a Schur functor argument. As a corollary of these results we obtain criteria for the Weyl modules and Specht modules of these algebras to be irreducible.

As a special case of our results we obtain, for the first time, an analogue of the Jantzen-Schaper theorem for Coxeter groups of type B.

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Andrew Mathas
10th January 1998.