Representations whose minimal reduction has a toric identity component

TL;DR

This paper classifies certain irreducible representations of compact Lie groups based on their orbit space geometry, linking them to non-polar representations with specific geometric actions.

Contribution

It provides a complete classification of irreducible representations with orbit spaces isometric to those of toric group extensions, identifying their geometric and symmetry properties.

Findings

Representations preserving an isoparametric submanifold

Representations acting with cohomogeneity one on the submanifold

Orbit spaces are isometric to those of finite extension of toric groups

Abstract

We classify irreducible representations of connected compact Lie groups whose orbit space is isometric to the orbit space of a representation of a finite extension of (positive dimensional) toric group. They turn out to be exactly the non-polar irreducible representations preserving an isoparametric submanifold and acting with cohomogeneity one on it.