Charges via the Affine Grassmannian

Abstract

We give a new construction of Lascoux-Schützenberger'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.

This version includes an expanded treatment of the first two chapters. The results on type A have been relocated to arXiv:2412.10562