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

• Autores: Dikran B. Karagueuzian, Peter Symonds
• Localización: Journal of the American Mathematical Society, ISSN 0894-0347, Vol. 20, Nº 4, 2007, págs. 931-967
• Idioma: inglés
• DOI: 10.1090/s0894-0347-07-00563-2
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• Resumen

  • 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.