A Note On Polar Representations

TL;DR

This paper demonstrates how to determine the polar representation of a compact connected Lie group using its dimension and isotropy subgroup data, even in reducible cases.

Contribution

It provides a method to linearly identify polar representations from basic group data in the reducible setting.

Findings

Polar representations can be reconstructed from dimension and isotropy subgroup data.

The method applies to reducible cases, broadening previous understanding.

Provides a linear determination approach for compact connected Lie groups.

Abstract

We show how a polar representation of a compact connected Lie group can be linearly determined from its dimension and isotropy subgroup data in the general reducible case.