Dimer models on cylinders over Dynkin diagrams and cluster algebras
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- by Maitreyee C. Kulkarni PDF
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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.References
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Additional Information
- Maitreyee C. Kulkarni
- Affiliation: Department of Mathematics, Louisiana State University, Baton Rouge, Louisiana
- Email: mkulka2@ias.edu
- Received by editor(s): September 6, 2017
- Received by editor(s) in revised form: March 29, 2018
- Published electronically: December 7, 2018
- Additional Notes: The author was supported by the NSF grant DMS-1601862, and an LSU Dissertation Year Fellowship.
- Communicated by: Jerzy Weyman
- © Copyright 2018 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 147 (2019), 921-932
- MSC (2010): Primary 16F30; Secondary 05E10
- DOI: https://doi.org/10.1090/proc/14344
- MathSciNet review: 3896043