English

Newton-Okounkov polytopes of flag varieties for classical groups

Algebraic Geometry 2019-02-08 v1

Abstract

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. In types A and C, we identify the corresponding Newton-Okounkov polytopes with the Feigin-Fourier-Littelmann-Vinberg polytopes. In types B and D, we compute low-dimensional examples and formulate open questions.

Keywords

Cite

@article{arxiv.1902.02511,
  title  = {Newton-Okounkov polytopes of flag varieties for classical groups},
  author = {Valentina Kiritchenko},
  journal= {arXiv preprint arXiv:1902.02511},
  year   = {2019}
}

Comments

15 pages, 1 figure