The charge statistic in type A via the Affine Grassmannian

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