We study coadjoint orbitopes, i.e. convex hulls of coadjoint orbits of compact Lie groups. We show that up to conjugation the faces are completely determined by the geometry of the faces of the convex hull of Weyl group orbits. We also consider the geometry of the faces and show that they are themselves coadjoint orbitopes. From the complex geometric point of view the sets of extreme points of a face are realized as compact orbits of parabolic subgroups of the complexified group.
Biliotti, L., Ghigi, A., Heinzner, P. (2014). Coadjoint orbitopes. OSAKA JOURNAL OF MATHEMATICS, 51(4), 935-969.
Coadjoint orbitopes
GHIGI, ALESSANDRO CALLISTOSecondo
;
2014
Abstract
We study coadjoint orbitopes, i.e. convex hulls of coadjoint orbits of compact Lie groups. We show that up to conjugation the faces are completely determined by the geometry of the faces of the convex hull of Weyl group orbits. We also consider the geometry of the faces and show that they are themselves coadjoint orbitopes. From the complex geometric point of view the sets of extreme points of a face are realized as compact orbits of parabolic subgroups of the complexified group.
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