Dimer models on cylinders over Dynkin diagrams and cluster algebras
Representation Theory
2017-07-13 v2 Combinatorics
Rings and Algebras
Abstract
In this paper, we describe a general setting for dimer models on cylinders over Dynkin diagrams which in type A reduces to the well studied case of dimer models on a disc. We prove that all Berenstein--Fomin--Zelevinsky quivers for Schubert cells in a symmetric Kac--Moody algebra give rise to dimer models on the cylinder over the corresponding Dynkin diagram. We also give an independent proof of a result of Buan, Iyama, Reiten and Smith that the corresponding superpotentials are rigid using the dimer model structure of the quivers.
Keywords
Cite
@article{arxiv.1704.07454,
title = {Dimer models on cylinders over Dynkin diagrams and cluster algebras},
author = {Maitreyee C. Kulkarni},
journal= {arXiv preprint arXiv:1704.07454},
year = {2017}
}