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Symmetric and exterior powers, linear source modules and representations of Schur superalgebras

Donkin, S. (2001) Symmetric and exterior powers, linear source modules and representations of Schur superalgebras. Proceedings of the London Mathematical Society, 83 (3). pp. 647-680. ISSN 1460-244X

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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.

Item Type: Article
Copyright, Publisher and Additional Information: © 2001 by London Mathematical Society.
Institution: The University of York
Academic Units: The University of York > Mathematics (York)
Depositing User: York RAE Import
Date Deposited: 27 Feb 2009 17:41
Last Modified: 27 Feb 2009 17:41
Published Version: http://dx.doi.org/10.1112/plms/83.3.647
Status: Published
Publisher: LMS Publications
Identification Number: 10.1112/plms/83.3.647
URI: http://eprints.whiterose.ac.uk/id/eprint/7354

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