Quantum Bruhat graph and Schubert polynomials

DOI10.1090/S0002-9939-04-07614-2zbMath1051.05078arXivmath/0206077MaRDI QIDQ4829889

Alexander Postnikov

Publication date: 1 December 2004

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0206077

zbMATH Keywords

quantum cohomologyBruhat orderSchubert classesquantum Bruhat graphpath Schubert polynomials

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)

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Affine approach to quantum Schubert calculus, Minimum quantum degrees for isotropic Grassmannians in types B and C, Quasi-homogeneity of the moduli space of stable maps to homogeneous spaces, Dimension formula for the affine Deligne-Lusztig variety \(X(\mu, b)\), Hofer-Zehnder capacity and Bruhat graph, Representation-theoretic interpretation of Cherednik-Orr's recursion formula for the specialization of nonsymmetric Macdonald polynomials at \(t = \infty\), Quantum cohomology of \(G/P\) and homology of affine Grassmannian, New structure on the quantum alcove model with applications to representation theory and Schubert calculus, Quantum \(K\)-theory Chevalley formulas in the parabolic case, Identities of inverse Chevalley type for the graded characters of level-zero Demazure submodules over quantum affine algebras of type \(C\), Generic Newton points and the Newton poset in Iwahori-double cosets, Quasi-homogeneity of the moduli space of stable maps to homogeneous spaces. II., Maximal Newton points and the quantum Bruhat graph, Euler characteristics in the quantum \(K\)-theory of flag varieties, A uniform realization of the combinatorial \(R\)-matrix for column shape Kirillov-Reshetikhin crystals, Specialization of nonsymmetric Macdonald polynomials at 𝑡=∞ and Demazure submodules of level-zero extremal weight modules, Affine Deligne-Lusztig varieties and quantum Bruhat graph, Curve neighborhoods and minimal degrees in quantum products

Cites Work

• On quantum cohomology rings of partial flag varieties
• Quantum double Schubert polynomials, quantum Schubert polynomials and Vafa-Intriligator formula
• Affine approach to quantum Schubert calculus
• Quantum Schubert polynomials
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