The paper constructs n-1 crystal embeddings of type A string polytopes and conjectures they yield n-1 atomic decompositions of B(kθ).
Charges via the Affine Grassmannian
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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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Unveiling Crystal Embeddings: New Perspectives on String Polytopes and Atomic Decompositions
The paper constructs n-1 crystal embeddings of type A string polytopes and conjectures they yield n-1 atomic decompositions of B(kθ).