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Harish-Chandra vertices and Steinberg's tensor product theorems for finite general linear groups

Published online by Cambridge University Press:  01 November 1997

R Dipper  and
J Du
R Dipper
Affiliation:
Mathematische Institut B, Universität Stuttgart, 70550 Stuttgart, Germany. E-mail: rdipper@methematik.uni-stuttgart.de
J Du
Affiliation:
School of Mathematics, University of New South Wales, Sydney 2052, Australia. E-mail: j.du@unsw.edu.au and jied@alpha.maths.unsw.edu.au
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Abstract

Representations of Hecke and $q$-Schur algebras are closely related to those of finite general linear groups $G$ in non-describing characteristics. Such a relationship can be described by certain functors. Using these functors, we determine the Harish-Chandra vertices and sources of certain indecomposable $G$-modules. The Green correspondence is investigated in this context. As a further application of our theory, we establish Steinberg's tensor product theorems for irreducible representations of $G$ in non-describing characteristics.

1991 Mathematics Subject Classification: 20C20, 20C33, 20G05, 20G40.

Keywords

Harish-Chandra vertextensor product theoremHecke algebra$q$-Schur algebrafinite general linear group
Type
Research Article
Information
Proceedings of the London Mathematical Society , Volume 75 , Issue 3 , November 1997 , pp. 559 - 599
Copyright
London Mathematical Society 1997

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