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

Karagueuzian, Dikran; Symonds, Peter

doi:10.1090/S0894-0347-07-00563-2

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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