The Jacobians and the discriminants of finite reflection groups (Q1822630)

Let S be the symmetric algebra of the dual space \(V^*\) of a K-vector space V, G a finite subgroup of GL(V) generated by reflections, \(R=S^ G\) the invariant subring of S under the action of G, and \(Der(S)^ G\) the R-module of G-invariant derivations of Der(S). As the main result in the present paper the author shows: \(Der(S)^ G\simeq D_ R(\delta)\) (as R-modules). Here \(\delta\) is the discriminant of G and \(D_ R(\delta)=\{\theta \in Der(R)|\) \(\theta(\delta)\in \delta R\}\). One of the corollaries of this theorem is: The reflection arrangement A(G) is a free arrangement.