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arXiv · 1704.07454

Dimer models on cylinders over Dynkin diagrams and cluster algebras

Maitreyee C. Kulkarni
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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.

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Maitreyee C. Kulkarni. 2017-07-11. Dimer models on cylinders over Dynkin diagrams and cluster algebras. https://arxiv.org/abs/1704.07454

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