Invariants of Finite Reflection Groups

Abstract

Let us define a reflection to be a unitary transformation, other than the identity, which leaves fixed, pointwise, a (reflecting) hyperplane, that is, a subspace of deficiency 1, and a reflection group to be a group generated by reflections. Chevalley (1) (and also Coxeter (2) together with Shephard and Todd (4)) has shown that a reflection group G, acting on a space of n dimensions, possesses a set of n algebraically independent (polynomial) invariants which form a polynomial basis for the set of all invariants of G.