2012/06/25 by Biliotti, Leonardo, Ghigi, Alessandro, Heinzner, Peter
#22E46 #53D20 #Differential Geometry (math.DG) #FOS: Mathematics #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.1206.5717
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.