Orbit spaces of compact coregular simple Lie groups with 2, 3 and 4 basic polynomial invariants: Effective tools in the analysis of invariant potentials

Abstract

The coregular real representations of the compact simple Lie groups are classified and the equalities and inequalities defining their orbit spaces are determined in the case of 2, 3 and 4 basic polynomial invariants. The results are obtained making use of the classification of the complex coregular simple Lie groups given by G. W. Schwarz and of the determination of all the allowable metric matrices for q-dimensional (q⩽4) orbit spaces of compact coregular linear groups, recently obtained by the present authors. The results are used to determine in a rigorous way the minima of two SO(10) and E6 invariant Higgs potentials.