September 19, Wednesday, 18:30, room 306 (note the change of time)

Valentina Kiritchenko

Polytopes in representation theory

I will talk about classical and new polytopes that arise in representation theory. Lattice points in these polytopes count basis vectors in irreducible representations of linear groups such as GL_n(\C), SO_n(\C) and Sp_{2n}(\C). In particular, I will review construction of Gelfand-Zetlin bases and the corresponding polytopes. Theory of Newton-Okounkov convex bodies provides an alternative (and probably simpler) method for constructing the same polytopes. For example, I will outline a construction of Feigin-Fourier-Littelmann-Vinberg polytopes as Newton-Okounkov polytopes of flag varieties. I will also discuss interpretation of Schubert calculus in terms of polytopes.

No preliminary knowledge of representation theory is required, all necessary definitions will be given during the talk.