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 (to appear).

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 Wmu for each multipartition mu of n. We
show that Wmu has simple head Fmu and that the set {Fmu}, 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.