Coadjoint orbitopes
Representation Theory
2013-04-19 v2 Symplectic Geometry
Abstract
We study coadjoint orbitopes, i.e. convex hulls of coadjoint orbits of a compact Lie group. We show that all the faces of such an orbitope are exposed. The face structure is studied by means of the momentum map and it is shown that every face is again a coadjoint orbitope. Up to conjugation the faces are completely determined by the momentum polytope and can be described in a simple way in terms of root data. Finally we consider the complex geometry of the coadjoint orbit and we prove that the submanifolds of the orbit that are extreme sets of a face are exactly the closed orbits of parabolic subgroups.
Cite
@article{arxiv.1110.6039,
title = {Coadjoint orbitopes},
author = {Leonardo Biliotti and Alessandro Ghigi and Peter Heinzner},
journal= {arXiv preprint arXiv:1110.6039},
year = {2013}
}
Comments
To appear on Osaka Journal of Mathematics