English

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

Representation Theory 2011-01-31 v6 Quantum Algebra

Abstract

In the current paper, we give a quiver theoretical interpretation of Mirkovi\'c-Vilonen polytopes in type AnA_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.

Keywords

Cite

@article{arxiv.1010.0086,
  title  = {Mirkovi\'c-Vilonen Polytopes and a quiver construction of crystal basis in type $A$},
  author = {Yoshihisa Saito},
  journal= {arXiv preprint arXiv:1010.0086},
  year   = {2011}
}

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29 pages