Mirković-Vilonen Polytopes and a quiver construction of crystal basis in type A

2010/10/01 by Yoshihisa Saito, Saito, Yoshihisa
Mathematics · #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Commutative Algebra and Its Applications #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1010.0086

openalex publication_date 2010/10/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In the current paper, we give a quiver theoretical interpretation of Mirković-Vilonen polytopes in type A_n. As a by-product, we give a new proof of the Anderson-Mirković conjecture which describes the explicit forms of the actions of lowering Kashiwara operators on the set of Mirković-Vilonen polytopes.

Citations

• Toward Berenstein-Zelevinsky data in affine type A, I: Construction of affine analogs

Related

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