The ABC's of affine Grassmannians and Hall-Littlewood polynomials

zbMATH Open1412.05215arXiv1605.05405MaRDI QIDQ5377440

Avinash J. Dalal, Jennifer Morse

Publication date: 24 May 2019

Abstract: We give a new description of the Pieri rule for k-Schur functions using the Bruhat order on the affine type-A Weyl group. In doing so, we prove a new combinatorial formula for representatives of the Schubert classes for the cohomology of affine Grassmannians. We show how new combinatorics involved in our formulas gives the Kostka-Foulkes polynomials and discuss how this can be applied to study the transition matrices between Hall-Littlewood and k-Schur functions.

Full work available at URL: https://arxiv.org/abs/1605.05405

zbMATH Keywords

Bruhat orderMacdonald polynomialsHall-Littlewood polynomialsPieri rule\(k\)-Schur functions\(k\)-tableaux

Mathematics Subject Classification ID

Combinatorial aspects of representation theory (05E10) Grassmannians, Schubert varieties, flag manifolds (14M15) Enumerative problems (combinatorial problems) in algebraic geometry (14N10)

Related Items (2)

Pieri rule for the affine flag variety ⋮ Newton polytopes of dual \(k\)-Schur polynomials

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