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تسجيل مستخدم جديدSchubert calculus on Newton-Okounkov polytopes
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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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We describe a new approach to the Schubert calculus on complete flag varieties using the volume polynomial associated with Gelfand-Zetlin polytopes. This approach allows us to compute the intersection products of Schubert cycles by intersecting faces of a polytope.
We compute the Newton--Okounkov bodies of line bundles on the complete flag variety of GL_n for a geometric valuation coming from a flag of translated Schubert subvarieties. The Schubert subvarieties correspond to the terminal subwords in the decompo
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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 r
elated 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.
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