Symplectic Gelfand-Zetlin polytopes and Schubert calculus

Chow rings of smooth projective toric varieties admit a convenient functorial description in terms of polytope rings introduced by Khovanskii and Pukhlikov. An analogous description for Chow rings of complete flag varieties was obtained by Kave and used by Kiritchenko, Smirnov and Timorin to get positive presentations of Schubert cycles by faces of a Gelfand-Zetlin polytope in type A. The underlying combinatorics was based on the mitosis of Knutson and Miller in type A. In my talk, I will describe a new mitosis algorithm on faces of a symplectic Gelfand-Zetlin polytope. Conjecturally, the collections of faces produced by this algoritm yield positive presentations of Schubert cycles in type C (joint work with Maria Padalko).Non UBCUnreviewedAuthor affiliation: National Research University Higher School of EconomicsFacult