November 28, Wednesday, 18:30, room 306

Valentina Kiritchenko

Newton-Okounkov polytopes of flag varieties for classical groups

For classical groups SL(n), SO(n) and Sp(2n), we define uniformly geometric valuations on the corresponding complete flag varieties. The valuation in every type comes from a natural coordinate system on the open Schubert cell, and is combinatorially related to the Gelfand-Zetlin pattern in the same type. For SL(n) and Sp(2n), we identify the corresponding Newton-Okounkov polytopes with the Feigin-Fourier-Littelmann-Vinberg polytopes. For SO(n), we compute low-dimensional examples and formulate open problems. All necessary definitions will be given in the talk.