Integrable systems and cluster algebras
Exactly Solvable and Integrable Systems
2024-03-13 v1 Mathematical Physics
Combinatorics
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.
Keywords
Cite
@article{arxiv.2403.07287,
title = {Integrable systems and cluster algebras},
author = {Michael Gekhtman and Anton Izosimov},
journal= {arXiv preprint arXiv:2403.07287},
year = {2024}
}
Comments
Written for Encyclopedia of Mathematical Physics (2nd edition). 26 pages, 14 figures