Quantum cohomology and the 𝑘-Schur basis

DOI10.1090/S0002-9947-07-04287-0zbMath1132.05060arXivmath/0501529OpenAlexW2143365249MaRDI QIDQ5437625

Jennifer Morse, Luc Lapointe

Publication date: 21 January 2008

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

Full work available at URL: https://arxiv.org/abs/math/0501529

zbMATH Keywords

quantum cohomologyLittlewood-Richardson coefficientsGrassmanian\(k\)-Schur functionsSchubert basis

Mathematics Subject Classification ID

Symmetric functions and generalizations (05E05) Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects) (14N35)

Related Items (25)

A \(k\)-tableau characterization of \(k\)-Schur functions ⋮ Symmetries on the lattice of \(k\)-bounded partitions ⋮ Equivariant \(K\)-theory of affine flag manifolds and affine Grothendieck polynomials ⋮ Charge on tableaux and the poset of \(k\)-shapes ⋮ Quantum cohomology of \(G/P\) and homology of affine Grassmannian ⋮ Combinatorics of the \(K\)-theory of affine grassmannians ⋮ Genus zero \(\widehat{\mathfrak{su}}(n)_m\) Wess-Zumino-Witten fusion rules via Macdonald polynomials ⋮ An affine approach to Peterson comparison ⋮ Demazure crystals and the Schur positivity of Catalan functions ⋮ Equivariant quantum Schubert polynomials ⋮ Schubert polynomials and \(k\)-Schur functions ⋮ Results and conjectures on the number of standard strong marked tableaux ⋮ The role of residue and quotient tables in the theory of \(k\)-Schur functions ⋮ Littlewood-Richardson coefficients for reflection groups. ⋮ Affine Pieri rule for periodic Macdonald spherical functions and fusion rings ⋮ Quantum and affine Schubert calculus and Macdonald polynomials ⋮ Affine insertion and Pieri rules for the affine Grassmannian ⋮ Unnamed Item ⋮ A recursion formula for \(k\)-Schur functions ⋮ The poset of $k$-shapes and branching rules for $k$-Schur functions ⋮ A filtration of \((q,t)\)-Catalan numbers ⋮ Catalan functions and 𝑘-Schur positivity ⋮ \(k\)-Schur expansions of Catalan functions ⋮ A non-commutative generalization of \(k\)-Schur functions ⋮ Pieri operators on the affine nilCoxeter algebra

Cites Work

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• Littlewood-Richardson coefficients for Hecke algebras at roots of unity
• The nil Hecke ring and cohomology of \(G/P\) for a Kac-Moody group \(G\)
• Quantum multiplication of Schur polynomials
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• Fermionic formulas for level-restricted generalized Kostka polynomials and coset branching functions
• Schur function analogs for a filtration of the symmetric function space
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• Enumeration of plane partitions
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• Applications of the Theory of Morse to Symmetric Spaces
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• Affine Stanley symmetric functions
• A Bruhat decomposition for the loop space of a compact group: A new approach to results of Bott
• Gromov-Witten invariants on Grassmannians
• The honeycomb model of 𝐺𝐿_{𝑛}(ℂ) tensor products II: Puzzles determine facets of the Littlewood-Richardson cone
• Schubert polynomials for the affine Grassmannian
• Quantum invariants of knots and 3-manifolds

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