Schubert calculus and Gelfand-Zetlin polytopes

DOI10.1070/RM2012v067n04ABEH004804zbMath1258.14055arXiv1101.0278OpenAlexW3100568056MaRDI QIDQ3145919

V. A. Kirichenko, Evgeny Smirnov, Vladlen Timorin

Publication date: 17 December 2012

Published in: Russian Mathematical Surveys (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1101.0278

zbMATH Keywords

Schubert calculusflag varietiesKogan facesChow ringvolume polynomialGelfand-Tsetlin polytopeDemazure Character formula

Mathematics Subject Classification ID

Lattice polytopes in convex geometry (including relations with commutative algebra and algebraic geometry) (52B20) Group actions on varieties or schemes (quotients) (14L30) Grassmannians, Schubert varieties, flag manifolds (14M15) Classical problems, Schubert calculus (14N15)

Related Items (20)

Grassmannians, flag varieties, and Gelfand–Zetlin polytopes ⋮ Brion's theorem for Gelfand-Tsetlin polytopes ⋮ Cohomology ring of the flag variety vs Chow cohomology ring of the Gelfand-Zetlin toric variety ⋮ On the number of faces of the Gelfand–Zetlin polytope ⋮ On the \(f\)-vectors of Gelfand-Cetlin polytopes ⋮ Marked poset polytopes: Minkowski sums, indecomposables, and unimodular equivalence ⋮ The diameter and automorphism group of Gelfand-Tsetlin polytopes ⋮ PBW filtration and monomial bases for Demazure modules in types A and C ⋮ The saturation problem for refined Littlewood-Richardson coefficients ⋮ Equivariant \(\mathbb{R}\)-test configurations and semistable limits of \(\mathbb{Q}\)-Fano group compactifications ⋮ Remixed Eulerian numbers ⋮ PBW-degenerated Demazure modules and Schubert varieties for triangular elements ⋮ Polyhedral realizations of crystal bases and convex-geometric Demazure operators ⋮ Polytopes and Large Counterexamples ⋮ The volume polynomial of regular semisimple Hessenberg varieties and the Gelfand-Zetlin polytope ⋮ Minuscule Schubert varieties: poset polytopes, PBW-degenerated Demazure modules, and Kogan faces ⋮ Gelfand--Tsetlin Polytopes: A Story of Flow and Order Polytopes ⋮ Schubert calculus from polyhedral parametrizations of Demazure crystals ⋮ \(W\)-translated Schubert divisors and transversal intersections ⋮ Schubert calculus on Newton-Okounkov polytopes

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