Integrable systems and cluster algebras
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866911793498030080 |
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| author | Gekhtman, Michael Izosimov, Anton |
| author_facet | Gekhtman, Michael Izosimov, Anton |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_07287 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Integrable systems and cluster algebras Gekhtman, Michael Izosimov, Anton Exactly Solvable and Integrable Systems Mathematical Physics Combinatorics 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. |
| title | Integrable systems and cluster algebras |
| topic | Exactly Solvable and Integrable Systems Mathematical Physics Combinatorics |
| url | https://arxiv.org/abs/2403.07287 |