Solutions of D_α- 0 from Homogeneous Invariant Functions

Abstract

We prove that the existence of a homogeneous invariant of degree n for a representation of a semi-simple Lie group guarantees the existence of non-trivial solutions of D_α = 0: these correspond to the maximum value of the square of the invariant divided by the norm of the representation to the n^{th} power.

4 pages, latex