TL;DR
This paper introduces a novel geometric approach to the charge statistic in type A, connecting it with the affine Grassmannian and crystal operators, providing new formulas and proofs independent of tableaux combinatorics.
Contribution
It offers a new geometric construction of the charge statistic and a formula based on modified crystal operators, with an independent proof.
Findings
New geometric construction of the charge statistic
A formula for charge in terms of modified crystal operators
An independent proof not relying on tableaux combinatorics
Abstract
We give a new construction of Lascoux-Sch\"utzenberger'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 not relying on tableaux combinatorics.
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