\(k\)-Schur functions and affine Schubert calculus

DOI10.1007/978-1-4939-0682-6zbMath1360.14004arXiv1301.3569OpenAlexW2139526676MaRDI QIDQ2442143

Mark Shimozono, Jennifer Morse, Anne Schilling, Luc Lapointe, Thomas Lam, Michael Zabrocki

Publication date: 31 March 2014

Published in: Fields Institute Monographs (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1301.3569

zbMATH Keywords

Schur functionsPieri rule\(k\)-Schur functionsaffine Schubert calculusKac-Moody varietyMacdonald positivitynilCoxeter ringnilHecke ring

Mathematics Subject Classification ID

Symmetric functions and generalizations (05E05) Combinatorial aspects of representation theory (05E10) Homogeneous spaces and generalizations (14M17) Research exposition (monographs, survey articles) pertaining to algebraic geometry (14-02) Basic orthogonal polynomials and functions associated with root systems (Macdonald polynomials, etc.) (33D52) Classical problems, Schubert calculus (14N15) Kac-Moody groups (20G44)

Related Items (24)

Symmetries on the lattice of \(k\)-bounded partitions ⋮ Pieri rule for the affine flag variety ⋮ Filtering cohomology of ordinary and Lagrangian Grassmannians ⋮ The Corners of Core Partitions ⋮ Charge on tableaux and the poset of \(k\)-shapes ⋮ Grothendieck-to-Lascoux expansions ⋮ Closed 𝑘-Schur Katalan functions as 𝐾-homology Schubert representatives of the affine Grassmannian ⋮ Affine nil-Hecke algebras and quantum cohomology ⋮ Genus zero \(\widehat{\mathfrak{su}}(n)_m\) Wess-Zumino-Witten fusion rules via Macdonald polynomials ⋮ An affine approach to Peterson comparison ⋮ Affine Permutations and an Affine Catalan Monoid ⋮ The role of residue and quotient tables in the theory of \(k\)-Schur functions ⋮ Keys and Demazure crystals for Kac-Moody algebras ⋮ A bijective proof of Macdonald's reduced word formula ⋮ Affine Pieri rule for periodic Macdonald spherical functions and fusion rings ⋮ On some factorization formulas of \(K\)-\(k\)-Schur functions ⋮ Alcove random walks, \(k\)-Schur functions and the minimal boundary of the \(k\)-bounded partition poset ⋮ Alcove random walks and \(k\)-Schur functions ⋮ A Pieri formula and a factorization formula for sums of \(K\)-theoretic \(K\)-Schur functions ⋮ Back stable Schubert calculus ⋮ Tropical methods in Hurwitz-Brill-Noether theory ⋮ Positivity of cylindric skew Schur functions ⋮ Combinatorial description of the cohomology of the affine flag variety ⋮ Newton polytopes in algebraic combinatorics

Uses Software

• SageMath
• Sage-Combinat

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