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Schubert Calculus on Newton–Okounkov Polytopes

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Interactions with Lattice Polytopes (ILP 2017)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 386))

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Abstract

A Newton–Okounkov polytope of a complete flag variety can be turned into a convex geometric model for Schubert calculus. Namely, we can represent Schubert cycles by linear combinations of faces of the polytope so that the intersection product of cycles corresponds to the set-theoretic intersection of faces (whenever the latter are transverse). We explain the general framework and survey particular realizations of this approach in types A, B and C.

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Acknowledgements

The study has been partially funded by the Russian Academic Excellence Project ‘5–100’.

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Authors and Affiliations

  1. Laboratory of Algebraic Geometry and Faculty of Mathematics, National Research University Higher School of Economics, Usacheva str. 6, 119048, Moscow, Russia

    Valentina Kiritchenko

  2. Institute for Information Transmission Problems, Moscow, Russia

    Valentina Kiritchenko

  3. SimilarWeb, Tel Aviv, Israel

    Maria Padalko

Authors
  1. Valentina Kiritchenko
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  2. Maria Padalko
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Correspondence to Valentina Kiritchenko .

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Editors and Affiliations

  1. School of Mathematical Sciences, University of Nottingham, Nottingham, UK

    Alexander M. Kasprzyk

  2. Fakultät für Mathematik, Otto-von-Guericke-Universität Magdeburg, Magdeburg, Sachsen-Anhalt, Germany

    Benjamin Nill

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Kiritchenko, V., Padalko, M. (2022). Schubert Calculus on Newton–Okounkov Polytopes. In: Kasprzyk, A.M., Nill, B. (eds) Interactions with Lattice Polytopes. ILP 2017. Springer Proceedings in Mathematics & Statistics, vol 386. Springer, Cham. https://doi.org/10.1007/978-3-030-98327-7_11

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