The puzzle conjecture for the cohomology of two-step flag manifolds

DOI10.1007/s10801-016-0697-3zbMath1356.05154arXiv1401.1725OpenAlexW2270033890WikidataQ123223725 ScholiaQ123223725MaRDI QIDQ2520759

Harry Tamvakis, Kevin Purbhoo, Andrew Kresch, Anders Skovsted Buch

Publication date: 16 December 2016

Published in: Journal of Algebraic Combinatorics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1401.1725

zbMATH Keywords

small quantum cohomologycohomology product structure constantspuzzle conjecturetwo-step flag manifolds

Mathematics Subject Classification ID

Symmetric functions and generalizations (05E05) Grassmannians, Schubert varieties, flag manifolds (14M15) Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects) (14N35) Classical problems, Schubert calculus (14N15)

Related Items (20)

EQUIVARIANT -THEORY OF GRASSMANNIANS ⋮ On cyclic descents for tableaux ⋮ Equivariant quantum cohomology of the Grassmannian via the rim hook rule ⋮ Quantum \(K\)-theory of incidence varieties ⋮ Schubert calculus and quiver varieties ⋮ Equivariant -theory of Grassmannians II: the Knutson–Vakil conjecture ⋮ Schubert polynomials and \(k\)-Schur functions ⋮ On equivariant quantum Schubert calculus for \(G/P\) ⋮ Positivity determines the quantum cohomology of Grassmannians ⋮ A puzzle formula for \(H^\ast_{T\times\mathbb C^{\times}}(T^\ast\mathbb P^n)\) ⋮ A representation-theoretic interpretation of positroid classes ⋮ Unique rectification in \(d\)-complete posets: towards the \(K\)-theory of Kac-Moody flag varieties ⋮ Quantum and affine Schubert calculus and Macdonald polynomials ⋮ Structure constants for Chern classes of Schubert cells ⋮ Restricting Schubert classes to symplectic Grassmannians using self-dual puzzles ⋮ A quotient of the ring of symmetric functions generalizing quantum cohomology ⋮ Vanishing of Littlewood-Richardson polynomials is in P ⋮ \(k\)-Schur expansions of Catalan functions ⋮ \(W\)-translated Schubert divisors and transversal intersections ⋮ Mutations of puzzles and equivariant cohomology of two-step flag varieties

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Product and puzzle formulae for \(GL_n\) Belkale-Kumar coefficients
• A Littlewood-Richardson rule for two-step flag varieties
• Puzzles, tableaux, and mosaics
• A Littelmann-type formula for Duistermaat-Heckman measures
• Puzzles and (equivariant) cohomology of Grassmannians
• Littlewood-Richardson rules for Grassmannians
• Pieri's formula for flag manifolds and Schubert polynomials
• Eigenvalue problem and a new product in cohomology of flag varieties
• A Littlewood-Richardson rule for factorial Schur functions
• Gromov-Witten invariants on Grassmannians
• The honeycomb model of 𝐺𝐿_{𝑛}(ℂ) tensor products II: Puzzles determine facets of the Littlewood-Richardson cone

This page was built for publication: The puzzle conjecture for the cohomology of two-step flag manifolds