The next meeting of the Joint Seminar of Analysis, Geometry and Topology Department will be held on January 19, 2016 at 14:00 in Room 478 of IMI.

A talk on:

Momentum images of representations

will be delivered by Elitza Hristova.

Everybody is invited.

Abstract. Let K be a compact semisimple Lie group, V an irreducible unitary representation of K, and P(V) the corresponding projective space. In this talk we consider the momentum map for the action of K on P(V) and discuss the question of describing the image of the momentum map for this action. By a theorem of Kirwan, the intersection of the momentum image with a positive Weyl chamber is a convex polytope, called the momentum polytope. In this talk, we are interested in describing the momentum polytope in terms of the highest weight of the representation. We start with a short introduction to the subject and a description of some known results and then we describe some of our results. The talk is based on a joint work with Valdemar Tsanov and Tomasz Maciazek.