Integrable systems and cluster algebras
arXiv:2403.07287
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.
Written for Encyclopedia of Mathematical Physics (2nd edition). 26 pages, 14 figures