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The module structure of a group action on a polynomial ring: A finiteness theorem


Authors: Dikran B. Karagueuzian and Peter Symonds
Journal: J. Amer. Math. Soc. 20 (2007), 931-967
MSC (2000): Primary 16W22; Secondary 20C20
DOI: https://doi.org/10.1090/S0894-0347-07-00563-2
Published electronically: April 11, 2007
MathSciNet review: 2328711
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Abstract: Consider a group acting on a polynomial ring over a finite field. We study the polynomial ring as a module for the group and prove a structure theorem with several striking corollaries. For example, any indecomposable module that appears as a summand must also appear in low degree, and so the number of isomorphism types of such summands is finite. There are also applications to invariant theory, giving a priori bounds on the degrees of the generators.


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Additional Information

Dikran B. Karagueuzian
Affiliation: Mathematics Department, Binghamton University, P.O. Box 6000, Binghamton, New York 13902-6000
Email: dikran@math.binghamton.edu

Peter Symonds
Affiliation: School of Mathematics, University of Manchester, P.O. Box 88, Manchester M60 1QD, United Kingdom
Email: Peter.Symonds@manchester.ac.uk

DOI: https://doi.org/10.1090/S0894-0347-07-00563-2
Received by editor(s): March 17, 2005
Published electronically: April 11, 2007
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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