The cyclotomic Jantzen-Schaper theorem
Gordon James and Andrew Mathas
Keywords Ariki-Koike algebras, cyclotomic
q-Schur algebras, Jantzen filtrations.
StatusTrans. AMS, 352 (2000), 5381-5404.
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
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