Name: The charge statistic in type A via the affine Grassmannian
Creator: Patimo, Leonardo
Keywords: Affine Grassmannian; Charge statistic; Kostka-Foulkes polynomials, FOS: Mathematics, Representation Theory (math.RT), Mathematics - Representation Theory

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Oct 2025Embargo end date: 01 Jan 2024 English Publisher:Elsevier BVJournal:Journal of Algebra, volume 679, pages 169-211 (issn: 0021-8693,

Authors: Patimo, Leonardo;

doi: 10.1016/j.jalgebra.2025.04.036 , 10.48550/arxiv.2412.10562

arXiv: http://arxiv.org/abs/2412.10562

handle: 11568/1314027

The charge statistic in type A via the affine Grassmannian

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Abstract

We give a new construction of Lascoux-Schüetzenberger's charge statistic in type A which is motivated by the geometric Satake equivalence. We obtain a new formula for the charge statistic in terms of modified crystal operators and an independent proof of this formula which does not rely on tableaux combinatorics.

expanded version, previously part of arXiv:2106.02564

Related Organizations

University of Pisa
Italy

Keywords

Affine Grassmannian; Charge statistic; Kostka-Foulkes polynomials, FOS: Mathematics, Representation Theory (math.RT), Mathematics - Representation Theory

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