The cyclotomic Jantzen-Schaper theorem


Gordon James and Andrew Mathas


Research Report 98-2
Date: 12 January 1998


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.

Key phrases

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

AMS Subject Classification (1991)

Primary: 16G99
Secondary: 20C20, 20G05


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