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The module structure of a group action on a polynomial ring: A finiteness theorem
Author(s):
Dikran
B.
Karagueuzian;
Peter
Symonds
Journal:
J. Amer. Math. Soc.
20
(2007),
931-967.
MSC (2000):
Primary 16W22;
Secondary 20C20
Posted:
April 11, 2007
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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:
10.1090/S0894-0347-07-00563-2
PII:
S 0894-0347(07)00563-2
Received by editor(s):
March 17, 2005
Posted:
April 11, 2007
Copyright of article:
Copyright
2007,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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