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SYMMETRIC AND EXTERIOR POWERS, LINEAR SOURCE MODULES AND REPRESENTATIONS OF SCHUR SUPERALGEBRAS

Published online by Cambridge University Press:  18 October 2001

STEPHEN DONKIN
STEPHEN DONKIN
Affiliation:
School of Mathematical Sciences, Queen Mary, University of London, Mile End Road, London E1 4NS, [email protected]
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Abstract

We study modules for the general linear group (over an infinite field of arbitrary characteristic) which are direct summands of tensor products of exterior powers and symmetric powers of the natural module. These modules, which we call listing modules, include the tilting modules and the injective modules for Schur algebras. The modules are studied via their relationship to linear source modules for symmetric groups on the one hand, and simple modules for Schur superalgebras on the other. Listing modules are parametrized by certain pairs of partitions. They are used to describe, by generators and relations, the Grothendieck ring of polynomial functors generated by the symmetric and exterior powers. We also (continuing work of J. Grabmeier) describe the vertices and sources of linear source modules for symmetric groups. 2000 Mathematical Subject Classification: 20G05, 20C30.

Keywords

general linear grouplinear source moduleSchur superalgebras
Type
Research Article
Information
Proceedings of the London Mathematical Society , Volume 83 , Issue 3 , November 2001 , pp. 647 - 680
Copyright
2001 London Mathematical Society

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