Polar symplectic representations

TL;DR

This paper classifies polar symplectic representations, showing they are coisotropic, and demonstrates that their moment maps separate closed orbits, extending results on multiplicity-free symplectic representations.

Contribution

It provides a classification of polar symplectic representations and analyzes their moment maps, linking to prior work on multiplicity-free symplectic representations.

Findings

Polar symplectic representations are coisotropic.

Moment maps separate closed orbits in these representations.

The work extends Knop's results to the polar case.

Abstract

We study polar representations in the sense of Dadok and Kac which are symplectic. We show that such representations are coisotropic and use this fact to give a classification. We also study their moment maps and prove that they separate closed orbits. Our work can also be seen as a specialization of some of the results of Knop on multiplicity free symplectic representations to the polar case.