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{
    "pk": 64901,
    "title": "Discrete dynamics in cluster integrable systems from geometric \\(R\\)-matrix transformations",
    "subtitle": null,
    "abstract": "Cluster integrable systems are a broad class of integrable systems modelled on bipartite dimer models on the torus. Many discrete integrable dynamics arise by applying sequences of local transformations, which form the cluster modular group of the cluster integrable system. This cluster modular group was recently characterized by the first author and Inchiostro. There exist some discrete integrable dynamics that make use of non-local transformations associated with geometric \\(R\\)-matrices. In this article we characterize the generalized cluster modular group - which includes both local and non-local transformations - in terms of extended affine symmetric groups. We also describe the action of the generalized cluster modular group on the spectral data associated with cluster integrable systems.\n \nMathematics Subject Classifications: 82B23, 13F60, 14H70, 20B35\n \nKeywords: Bipartite dimer model, cluster algebras, geometric \\(R\\)-matrices, discrete integrable systems, extended affine symmetric group",
    "language": "en",
    "license": {
        "name": "Creative Commons Attribution 4.0",
        "short_name": "CC BY 4.0",
        "text": "Attribution — You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.\n\nNo additional restrictions — You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.",
        "url": "https://creativecommons.org/licenses/by/4.0"
    },
    "keywords": [
        {
            "word": "Bipartite dimer model"
        },
        {
            "word": "cluster algebras"
        },
        {
            "word": "geometric \\(R\\)-matrices"
        },
        {
            "word": "discrete integrable systems"
        },
        {
            "word": "extended affine symmetric group"
        }
    ],
    "section": "Research Articles",
    "is_remote": true,
    "remote_url": "https://escholarship.org/uc/item/2z04v7bz",
    "frozenauthors": [],
    "date_submitted": "2023-09-14T08:00:47Z",
    "date_accepted": "2023-09-14T08:00:47Z",
    "date_published": "2023-09-15T07:00:00Z",
    "render_galley": null,
    "galleys": [
        {
            "label": "",
            "type": "pdf",
            "path": "https://journalpub.escholarship.org/combinatorial_theory/article/64901/galley/49711/download/"
        }
    ]
}