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Arnold Mathematical Journal

, Volume 5, Issue 2–3, pp 355–371 | Cite as

Newton–Okounkov Polytopes of Flag Varieties for Classical Groups

  • Valentina KiritchenkoEmail author
Research Contribution

Abstract

For classical groups \(SL_n(\mathbb {C})\), \(SO_n(\mathbb {C})\) and \(Sp_{2n}(\mathbb {C})\), 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

Newton–Okounkov convex body Flag variety FFLV polytope 

Notes

Acknowledgements

I am grateful to the referee for the careful reading of the paper and useful comments.

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Copyright information

© Institute for Mathematical Sciences (IMS), Stony Brook University, NY 2019

Authors and Affiliations

  1. 1.Laboratory of Algebraic Geometry and Faculty of Mathematics, National Research University Higher School of EconomicsRussian FederationMoscowRussia
  2. 2.Institute for Information Transmission ProblemsMoscowRussia

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