Un th\'eor\`eme de convexit\'e r\'eel pour les applications moment \`a valeurs dans un groupe de Lie

摘要

In this note, we state and give the main ideas of the proof of a realconvexity theorem for group-valued momentum maps. This result is aquasi-Hamiltonian analogue of the O'Shea-Sjamaar theorem in the usualHamiltonian setting. We prove here that the image under the momentum map of thefixed-point set of a form-reversing involution defined on a quasi-Hamiltonianspace is a convex polytope, that we describe as a subpolytope of the momentumpolytope.