Dimer models on cylinders over Dynkin diagrams and cluster algebras

Kulkarni, Maitreyee

doi:10.1090/proc/14344

Dimer models on cylinders over Dynkin diagrams and cluster algebras
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by Maitreyee C. Kulkarni PDF

Proc. Amer. Math. Soc. 147 (2019), 921-932 Request permission

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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