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Integrable systems and cluster algebras (2403.07287v1)

Published 12 Mar 2024 in nlin.SI, math-ph, math.CO, and math.MP

Abstract: We review several constructions of integrable systems with an underlying cluster algebra structure, in particular the Gekhtman-Shapiro-Tabachnikov-Vainshtein construction based on perfect networks and the Goncharov-Kenyon approach based on the dimer model. We also discuss results of Galashin and Pylyavskyy on integrability of T-systems.

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