On the orbit space of an irreducible representation of the special unitary group

TL;DR

This paper proves that the orbit space resulting from an irreducible representation of a special unitary group of rank greater than 1 cannot be a smooth manifold, highlighting a fundamental geometric property.

Contribution

It establishes a new result about the geometric structure of orbit spaces for irreducible representations of special unitary groups, specifically their non-smoothness.

Findings

Orbit space of such representations is not a smooth manifold.

The result applies to groups of rank greater than 1.

Provides insight into the geometric complexity of representation orbit spaces.

Abstract

We prove that the quotient of an irreducible representation of a special unitary group of rank greater than 1 cannot be a smooth manifold.