DIMER MODELS ON CYLINDERS OVER DYNKIN DIAGRAMS AND CLUSTER ALGEBRAS.

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. [ABSTRACT FROM AUTHOR]