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

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.

29 pages

References in corpus (1)

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