Mutations of puzzles and equivariant cohomology of two-step flag varieties

DOI10.4007/annals.2015.182.1.4zbMath1354.14072arXiv1401.3065OpenAlexW2963177897MaRDI QIDQ2352908

Anders Skovsted Buch

Publication date: 6 July 2015

Published in: Annals of Mathematics. Second Series (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1401.3065

zbMATH Keywords

puzzlesSchubert calculusquantum cohomologyGromov-Witten invariantGrassmann varietytwo-step flag varietyequivariant Schubert structure constantmutation algorithm

Mathematics Subject Classification ID

Combinatorial aspects of representation theory (05E10) Grassmannians, Schubert varieties, flag manifolds (14M15) Other algebro-geometric (co)homologies (e.g., intersection, equivariant, Lawson, Deligne (co)homologies) (14F43)

Related Items (17)

EQUIVARIANT -THEORY OF GRASSMANNIANS ⋮ Equivariant Pieri rules for isotropic Grassmannians ⋮ An equivariant quantum Pieri rule for the Grassmannian on cylindric shapes ⋮ Equivariant quantum cohomology of the Grassmannian via the rim hook rule ⋮ A Molev-Sagan type formula for double Schubert polynomials ⋮ Quantum \(K\)-theory of incidence varieties ⋮ Schubert calculus and quiver varieties ⋮ On Schubert’s Problem of Characteristics ⋮ Equivariant -theory of Grassmannians II: the Knutson–Vakil conjecture ⋮ On equivariant quantum Schubert calculus for \(G/P\) ⋮ Positivity determines the quantum cohomology of Grassmannians ⋮ Unique rectification in \(d\)-complete posets: towards the \(K\)-theory of Kac-Moody flag varieties ⋮ Quantum and affine Schubert calculus and Macdonald polynomials ⋮ Schubert structure operators ⋮ A geometric proof of an equivariant Pieri rule for flag manifolds ⋮ \(W\)-translated Schubert divisors and transversal intersections ⋮ Twisted Schubert polynomials

Cites Work

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• Product and puzzle formulae for \(GL_n\) Belkale-Kumar coefficients
• Quantum \(K\)-theory of Grassmannians
• Littlewood-Richardson polynomials
• A Littlewood-Richardson rule for two-step flag varieties
• The nil Hecke ring and cohomology of \(G/P\) for a Kac-Moody group \(G\)
• A Littelmann-type formula for Duistermaat-Heckman measures
• Puzzles and (equivariant) cohomology of Grassmannians
• The saturation conjecture (after A. Knutson and T. Tao). With an appendix by William Fulton
• Positivity in equivariant Schubert calculus.
• Gromov-Witten classes, quantum cohomology, and enumerative geometry
• Curve neighborhoods of Schubert varieties
• On equivariant quantum cohomology of homogeneous spaces: Chevalley formulae and algorithms
• Equivariant quantum Schubert calculus
• The puzzle conjecture for the cohomology of two-step flag manifolds
• Kostant polynomials and the cohomology ring for  G / B
• The Geometry of Flag Manifolds
• Equivariant Littlewood-Richardson skew tableaux
• A Littlewood-Richardson rule for factorial Schur functions
• Notes on stable maps and quantum cohomology
• Gromov-Witten invariants on Grassmannians
• The honeycomb model of 𝐺𝐿_{𝑛}(ℂ) tensor products II: Puzzles determine facets of the Littlewood-Richardson cone
• Positivity in equivariant quantum Schubert calculus
• A mathematical theory of quantum cohomology

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