Polar orbitopes
Representation Theory
2013-04-24 v2 Differential Geometry
Abstract
We study polar orbitopes, i.e. convex hulls of orbits of a polar representation of a compact Lie group. The face structure is studied by means of the gradient momentum map and it is shown that every face is exposed and is again a polar orbitope. Up to conjugation the faces are completely determined by the momentum polytope. There is a tight relation with parabolic subgroups: the set of extreme points of a face is the closed orbit of a parabolic subgroup of G and for any parabolic subgroup the closed orbit is of this form.
Cite
@article{arxiv.1206.5717,
title = {Polar orbitopes},
author = {Leonardo Biliotti and Alessandro Ghigi and Peter Heinzner},
journal= {arXiv preprint arXiv:1206.5717},
year = {2013}
}
Comments
24 pages. To appear on Communications in Analysis and Geometry