2016/11/17 by Kobert, Tim
#Algebraic Geometry (math.AG) #FOS: Mathematics #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.1611.05658
Let G be a Lie group with real semisimple Lie algebra \mathfrakg. Further let \mathfrakg = \mathfrakk ⊕ \mathfrakp be a Cartan decomposition. The maximal compact subgroup K ⊆ G acts on \mathfrakp via the adjoint representation and the convex hulls of the resulting orbits are the polar orbitopes. We prove that every polar orbitope is a spectrahedron by giving an explicit representation. In addition we give a new proof for the fact that the faces of a polar orbitope are, up to conjugation, given by the faces of the momentum polytope.