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Proceedings of the London Mathematical Society 1998 77(2):327-361; doi:10.1112/S0024611598000483
© 1998 by London Mathematical Society
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© London Mathematical Society

The (Q, q)-Schur Algebra

R Dipper, G James and A Mathas

Mathematische Institut B, Universität Stuttgart Postfach 80 11 40, 70550 Stuttgart, Germany. E-mail: rdipper{at}mathematik.uni-stuttgart.de
Department of Mathematics, Imperial College Huxley Building, 180 Queen's Gate, London SW7 2BZ, UK. g.james{at}ic.ac.uk

Received 12 December 1996. Revision received 5 June 1997.

In this paper we use the Hecke algebra of type B to define a new algebra S which is an analogue of the q-Schur algebra. We show that S has ‘generic’ basis which is independent of the choice of ring and the parameters q and Q. We then construct Weyl modules for S and obtain, as factor modules, a family of irreducible S-modules defined over any field. 1991 Mathematics Subject Classification: 16G99, 20C20, 20G05.

Key Words: Hecke algebras • Schur algebras • Coxeter groups

Present address: School of Mathematics, University of Sydney, N.S.W. 2006, Australia. E-mail: mathas{at}maths.usyd.edu.au


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