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Truncated symmetric powers and modular representations of GLn

Published online by Cambridge University Press:  24 October 2008

Stephen Doty  and
Grant Walker
Stephen Doty
Affiliation:
Department of Mathematical Sciences, Loyola University of Chicago, 6525 N. Sheridan Road, Chicago, Illinois 60626, U.S.A.
Grant Walker
Affiliation:
Department of Mathematics, University of Manchester, Oxford Road, Manchester M13 9PL
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Abstract

Several results are obtained relating to the modular representation theory of the general linear group GLn in the defining characteristic p > 0. In Section 1, embeddings of certain simple modules in symmetric powers of the natural module, or in tensor products of truncated symmetric powers, are constructed. In Section 2, cases are found where simple quotientsof Schur modules H0(λ) can be constructed by extending theidea of truncation to these modules in a natural way. In Section 3, the characters of those simple modules which can be constructed as twisted tensor products of truncated symmetric powers are expressed in terms of Schur functions.

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Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 119 , Issue 2 , February 1996 , pp. 231 - 242
Copyright
Copyright © Cambridge Philosophical Society 1996

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