Degree
Doctor of Philosophy (PhD)
Department
Mathematics
Document Type
Dissertation
Abstract
This dissertation describes 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.
Date
6-25-2018
Recommended Citation
Kulkarni, Maitreyee Chandramohan, "Dimers on Cylinders over Dynkin Diagrams and Cluster Algebras" (2018). LSU Doctoral Dissertations. 4642.
https://repository.lsu.edu/gradschool_dissertations/4642
Committee Chair
Yakimo, Milen
DOI
10.31390/gradschool_dissertations.4642