Invariants of Finite Reflection Groups

Abstract

Let K be a field of characteristic zero. Let V be an n -dimensional vector space over K and let S be the graded ring of polynomial functions on V . If G is a group of linear transformations of V , then G acts naturally as a group of automorphisms of S if we define The elements of S invariant under all γ ∈ G constitute a homogeneous subring I(S) of S called the ring of polynomial invariants of G .