Seminarium "The Trans-Carpathian Seminar on Geometry & Physics"

I will present our recent results concerning the problem of approximating the momentum polytope for irreducible unitary representations of connected compact semisimple Lie groups. I will outline our motivation, which comes from the formulation of the quantum marginal problem of describing spectra of reduced quantum states in terms of the image of a momentum map. The approximations of the momentum polytope that we consider stem from studying the structure of the momentum image around the highest weight of the representation at hand. These are mainly representations of local unitary groups in systems with a fixed number of particles.