# Quasi-Hamiltonian model spaces

## TL;DR

This paper classifies quasi-Hamiltonian model spaces for simple, simply connected compact Lie groups, identifying subgroups related to multiplicity free manifolds with surjective momentum maps, based on F. Knop's classification.

## Contribution

It explicitly identifies subgroups of the Lie algebra of the maximal torus corresponding to quasi-Hamiltonian model spaces, extending the classification framework.

## Key findings

- Explicit subgroup classifications for quasi-Hamiltonian model spaces.
- Connection with F. Knop's classification of multiplicity free manifolds.
- Provides a comprehensive list of isomorphism classes for these spaces.

## Abstract

Let K be a simple and simply connected compact Lie group. We call a (twisted) quasi-Hamiltonian K-manifold M a quasi-Hamiltonian model space if it is multiplicity free and its momentum map is surjective. We explicitly identify the subgroups of the Lie algebra of the maximal torus of K, which, by F. Knop's classification of multiplicity free quasi-Hamiltonian manifolds, are in one-to-one correspondence with the isomorphism classes of quasi-Hamiltonian model K-spaces.