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arXiv · 1010.0086

Mirkovi\'c-Vilonen Polytopes and a quiver construction of crystal basis in type $A$

Yoshihisa Saito
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Abstract

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

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BibTeXRIS

Yoshihisa Saito. 2010-10-01. Mirkovi\'c-Vilonen Polytopes and a quiver construction of crystal basis in type $A$. https://arxiv.org/abs/1010.0086

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