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The (Q,q)-Schur algebra

Published online by Cambridge University Press:  01 September 1998

R Dipper ,
G James  and
A Mathas
R Dipper
Affiliation:
Mathematische Institut B, Universität Stuttgart, Postfach 80 11 40, 70550 Stuttgart, Germany. E-mail: [email protected]
G James
Affiliation:
Department of Mathematics, Imperial College, Huxley Building, 180 Queen's Gate, London SW7 2BZ, UK. [email protected]
A Mathas
Affiliation:
Department of Mathematics, Imperial College, Huxley Building, 180 Queen's Gate, London SW7 2BZ, UK. [email protected] Present address: School of Mathematics, University of Sydney, N.S.W. 2006, Australia. E-mail: [email protected]
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Abstract

In this paper we use the Hecke algebra of type $\bf B$ to define a new algebra $\mathcal S$ which is an analogue of the $q$-Schur algebra. We show that $\mathcal S$ has ‘generic’ basis which is independent of the choice of ring and the parameters $q$ and $Q$. We then construct Weyl modules for $\mathcal S$ and obtain, as factor modules, a family of irreducible $\mathcal S$-modules defined over any field.

1991 Mathematics Subject Classification: 16G99, 20C20, 20G05.

Keywords

Hecke algebrasSchur algebrasCoxeter groups
Type
Research Article
Information
Proceedings of the London Mathematical Society , Volume 77 , Issue 2 , September 1998 , pp. 327 - 361
Copyright
London Mathematical Society 1998

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