Invariant convex sets in polar representations
Complex Variables
2014-11-25 v1 Differential Geometry
Abstract
We study a compact invariant convex set in a polar representation of a compact Lie group. Polar rapresentations are given by the adjoint action of on , where is a maximal compact subgroup of a real semisimple Lie group with Lie algebra . If is a maximal abelian subalgebra, then is a convex set in . We prove that up to conjugacy the face structure of is completely determined by that of and that a face of is exposed if and only if the corresponding face of is exposed. We apply these results to the convex hull of the image of a restricted momentum map.
Cite
@article{arxiv.1411.6041,
title = {Invariant convex sets in polar representations},
author = {Leonardo Biliotti and Alessandro Ghigi and Peter Heinzner},
journal= {arXiv preprint arXiv:1411.6041},
year = {2014}
}