Title:   The cyclotomic Jantzen-Schaper theorem.
Authors: Gordon James and Andrew Mathas.

Keywords: Ariki-Koike algebras, cyclotomic $q$-Schur algebras, 
          Jantzen filtrations.

Status:   Trans. AMS, (to appear).

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.