Free Modules of Relative Invariants of Finite Groups

摘要

This paper addresses questions about when modules of relative invariants of a finite groupGacting on a polynomial ringRare free over the ring of invariant polynomialsRG. 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 charactersχof degree one have the above property, and deduce from this a characterization of whichGhave the above property for all their degree one characte