Four Dimensional Orbit Spaces of Compact Coregular Linear Groups

TL;DR

This paper classifies all four-dimensional orbit spaces of compact coregular linear groups using a universal differential equation, revealing universal properties relevant to classical spontaneous symmetry breaking in physics.

Contribution

It provides a complete classification of four-dimensional orbit spaces for these groups by solving a universal differential equation, a novel approach in the field.

Findings

All four-dimensional orbit spaces of compact coregular linear groups are determined.

The method involves integrating a universal differential equation based on the integrity basis.

Results highlight universality properties in classical spontaneous symmetry breaking.

Abstract

All four dimensional orbit spaces of compact coregular linear groups have been determined. The results are obtained through the integration of a universal differential equation, that only requires as input the number of elements of an integrity basis of the ideal of polynomial invariants of the linear group. Our results are relevant and lead to universality properties in the physics of spontaneous symmetry breaking at the classical level.