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Free Modules of Relative Invariants of Finite Groups
Author(s) -
Reiner Victor
Publication year - 1989
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1002/sapm1989812181
Subject(s) - converse , mathematics , characterization (materials science) , invariant (physics) , property (philosophy) , pure mathematics , degree (music) , ring (chemistry) , finite group , polynomial , group (periodic table) , combinatorics , algebra over a field , discrete mathematics , mathematical analysis , geometry , physics , philosophy , chemistry , organic chemistry , epistemology , quantum mechanics , acoustics , optics , mathematical physics
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 R G . 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.
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