## Cyclotomic *q*-Schur algebras

### Richard Dipper, Gordon James and Andrew Mathas

#### Keywords

Ariki-Koike algebras, cyclotomic Hecke algebras, Schur algebras, cellular algebras

#### Status

*Math. Zeitschrift*, **229** (1998), 385-416.

MR2000a:20033

#### Abstract

Recently, we [DJM] and, independently, Du and
Scott [DS], defined an analogue of the *q*-Schur algebra for an
Iwahori-Hecke algebra of type **B**. In this paper we study an
analogue *S* of the *q*-Schur algebra for an arbitrary
Ariki-Koike algebra; we call this algebra the **cyclotomic
***q*-Schur algebra.
We first construct a cellular basis for the cyclotomic
*q*-Schur algebra. As a consequence we obtain a Weyl module
*W*^{mu} for each multipartition *mu* of
*n*. We show that *W*^{mu} has simple head
*F*^{mu} and that the set {*F*^{mu}}, as
*mu* ranges over the multipartitions of *n*, is a complete set
of non-isomorphic irreducible *S*-modules. Using the cellular structure
of *S*, it is now easy to see that the cyclotomic *q*-Schur algebra is quasi-hereditary.

The paper is available as gzipped
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*Andrew Mathas*

15th August 1997.