Free Modules of Relative Invariants of Finite Groups

Victor Reiner

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2 Scopus citations


This paper addresses questions about when modules of relative invariants of a finite group G acting on a polynomial ring R are free over the ring of invariant polynomials RG. A converse (first obtained by Shchvartsman) is proven of a result asserting that these modules are always free when the group is generated by pseudoreflections. We also re-prove the characterization given by Shchvartsman of which characters χ of degree one have the above property, and deduce from this a characterization of which G have the above property for all their degree one characters.

Original languageEnglish (US)
Pages (from-to)181-184
Number of pages4
JournalStudies in Applied Mathematics
Issue number2
StatePublished - Oct 1 1989

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