Moment polytopes in real symplectic geometry I

TL;DR

This paper explores the structure of moment polytopes in real symplectic geometry, specifically how to parameterize the facets of the real part of a Kähler Hamiltonian manifold using real Ressayre's pairs.

Contribution

It introduces a method to parameterize the equations of the facets of the real moment polytope via real Ressayre's pairs, extending previous geometric results.

Findings

Parameterization of facet equations of Delta(Z)

Connection between real Ressayre's pairs and moment polytopes

Extension of O'Shea-Sjamaar's theorem to explicit facet descriptions

Abstract

Let Z be the real part of a K{\"a}hler Hamiltonian manifold M. The O'Shea-Sjamaar's Theorem tells us that the moment polytope Delta(Z) corresponds to the anti-invariant part of the Kirwan polytope Delta(M). The purpose of the present paper is to explain how to parameterize the equations of the facets of Delta(Z) in terms of real Ressayre's pairs of Z.