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

Karagueuzian, Dikran¹ ; Symonds, Peter²

¹ Mathematics Department, Binghamton University, P.O. Box 6000, Binghamton, New York 13902-6000
² School of Mathematics, University of Manchester, P.O. Box 88, Manchester M60 1QD, United Kingdom

Journal of the American Mathematical Society, Tome 20 (2007) no. 4, pp. 931-967

Résumé

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.

Détail

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

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