Invariants of finite reflection groups

Abstract

The invariants of a finite reflection group acting on an n dimensional vector space over a field of characteristic zero have an integrity basis or n invariants. If the underlying field is real or complex this property is a characterization of the finite reflection groups. In this thesis the above statement is proved and we give a method for computing the degrees of the members of the basis. __The construction of a basic set of invariants is shown to be related to the solution of a certain mean value problem. Considerations of this mean value problem lead to a conjecture yielding an explicit construction of a basic set of invariants. The conjecture is verified for most of the irreducible finite reflection groups.