The cluster modular group of the dimer model
Terrence George
University of Michigan, Ann Arbor, USAGiovanni Inchiostro
University of Washington, Seattle, USA
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Abstract
Associated to a convex integral polygon is a cluster integrable system constructed from the dimer model. We compute the group of symmetries of , called the (2-2) cluster modular group, showing that it is a certain abelian group conjectured by Fock and Marshakov. Combinatorially, non-torsion elements of are ways of shuffling the underlying bipartite graph, generalizing domino-shuffling. Algebro-geometrically, is a subgroup of the Picard group of a certain algebraic surface associated to .
Cite this article
Terrence George, Giovanni Inchiostro, The cluster modular group of the dimer model. Ann. Inst. Henri Poincaré Comb. Phys. Interact. 11 (2024), no. 1, pp. 147–198
DOI 10.4171/AIHPD/164