# The cyclotomic Jantzen-Schaper theorem

## Authors

**Gordon James** and **Andrew Mathas**

## Status

Research Report 98-2

Date: 12 January 1998

## 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**.

## Key phrases

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

## AMS Subject Classification (1991)

Primary: 16G99

Secondary: 20C20, 20G05

## Content

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