On the orbit spaces of irreducible representations of simple compact Lie groups of types B, C, and D

TL;DR

This paper investigates the conditions under which the orbit space of an irreducible representation of certain simple compact Lie groups can be a smooth manifold, establishing that this occurs only in two specific cases.

Contribution

It provides a classification result showing that the orbit space is a smooth manifold only in two particular instances for groups of types B, C, and D.

Findings

Orbit space is a smooth manifold in only two cases.

Focus on irreducible representations of types B, C, and D.

Provides a classification of when the orbit space is smooth.

Abstract

It is proved that the orbit space of an irreducible representation of a simple connected compact Lie group of type B, C, or D can be a smooth manifold only in two cases.