Hostname: page-component-76fb5796d-r6qrq Total loading time: 0 Render date: 2024-04-26T06:05:03.948Z Has data issue: false hasContentIssue false
  • English
  • Français

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: rdipper@mathematik.uni-stuttgart.de
G James
Affiliation:
Department of Mathematics, Imperial College, Huxley Building, 180 Queen's Gate, London SW7 2BZ, UK. g.james@ic.ac.uk
A Mathas
Affiliation:
Department of Mathematics, Imperial College, Huxley Building, 180 Queen's Gate, London SW7 2BZ, UK. g.james@ic.ac.uk Present address: School of Mathematics, University of Sydney, N.S.W. 2006, Australia. E-mail: mathas@maths.usyd.edu.au
Get access

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)