Momentum polytopes of rank one for multiplicity free quasi-Hamiltonian manifolds

TL;DR

This paper classifies all rank-one momentum polytopes for multiplicity free quasi-Hamiltonian manifolds associated with simple, simply connected Lie groups, expanding the catalog of known examples and methods in symplectic geometry.

Contribution

It provides a complete classification of rank-one momentum polytopes for these manifolds using advanced methods, introducing many new explicit examples.

Findings

Complete classification of rank-one momentum polytopes.

Identification of numerous new examples of multiplicity free manifolds.

Application of recent methods by F. Knop to this classification.

Abstract

We classify all momentum polytopes of rank one for multiplicity free quasi-Hamiltonian $K$-manifolds for simple and simply connected Lie groups $K$ by using the methods developed in a recent paper by F. Knop. This leads to lots of new concrete examples of multiplicity free quasi-Hamiltonian manifolds or equivalently, Hamiltonian loop group actions.