Cyclotomic q-Schur algebras

Richard Dipper, Gordon James and Andrew Mathas


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


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


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.

The paper is available as gzipped dvi (50 kB) and postscript (180 kB) files.

Alternatively, you can request a copy by e-mailing me.

Andrew Mathas
15th August 1997