Finite Reflection Groups in Characteristic Zero

Abstract

From now on we keep the notation previously introduced: V is an r–dimensional vector space over the characteristic 0 field k, S is the symmetric algebra of V, $\mathfrak{N}$ is its maximal graded ideal, G is a finite subgroup of GL(V), Ref(G) is the set of reflections in G, R = S ^G is the invariant algebra, $\mathfrak{M}$ is its maximal graded ideal, S _G := S/$\mathfrak{M}$ S is the coinvariant algebra.