Closed 𝑘-Schur Katalan functions as 𝐾-homology Schubert representatives of the affine Grassmannian

DOI10.1090/btran/184arXiv2203.14483MaRDI QIDQ6126699

Takeshi Ikeda, Shinsuke Iwao, Satoshi Naito

Publication date: 9 April 2024

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

Full work available at URL: https://arxiv.org/abs/2203.14483

zbMATH Keywords

symmetric functionsaffine GrassmannianKatalan function\(K\textit{-}k\)-Schur

Mathematics Subject Classification ID

Symmetric functions and generalizations (05E05) Grassmannians, Schubert varieties, flag manifolds (14M15) Classical problems, Schubert calculus (14N15)

Cites Work

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• Combinatorics of the \(K\)-theory of affine grassmannians
• Quantum and affine Schubert calculus and Macdonald polynomials
• A short derivation of the Möbius function for the Bruhat order.
• Quantum cohomology of flag manifolds \(G/B\) and quantum Toda lattices.
• Schubert varieties and degeneracy loci
• Quantum \(K\)-theory on flag manifolds, finite-difference Toda lattices and quantum groups
• Affine Stanley symmetric functions for classical types
• A conjectural Peterson isomorphism in \(K\)-theory
• Quantum double Schubert polynomials, quantum Schubert polynomials and Vafa-Intriligator formula
• Chevalley formula for anti-dominant weights in the equivariant \(K\)-theory of semi-infinite flag manifolds
• Quantum \(K\) theory of symplectic Grassmannians
• Schubert polynomials for the affine Grassmannian of the symplectic group
• A Pieri formula and a factorization formula for sums of \(K\)-theoretic \(K\)-Schur functions
• From quantum Schubert polynomials to \(k\)-Schur functions via the Toda lattice
• \(k\)-double Schur functions and equivariant (co)homology of the affine Grassmannian
• \(k\)-Schur functions and affine Schubert calculus
• Tableaux on \(k+1\)-cores, reduced words for affine permutations, and \(k\)-Schur expansions
• \(K\)-theoretic Catalan functions
• Nonlinear Partial Difference Equations. II. Discrete-Time Toda Equation
• Combinatorics of Coxeter Groups
• K-theory Schubert calculus of the affine Grassmannian
• The discrete Toda equation revisited: dualβ-Grothendieck polynomials, ultradiscretization, and static solitons
• A Chevalley formula for the equivariant quantum $K$-theory of cominuscule varieties
• Equivariant homology and K-theory of affine Grassmannians and Toda lattices
• Peterson Isomorphism in K-theory and Relativistic Toda Lattice
• Affine Weyl Groups in K-Theory and Representation Theory
• On the Finiteness of Quantum K-Theory of a Homogeneous Space