{"paper":{"title":"Integrable systems inspired by DAHA and DIM algebra: type $C^\\vee C$ versus type $A$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.QA"],"primary_cat":"hep-th","authors_text":"A. Mironov, A. Popolitov, L. Bishler","submitted_at":"2026-07-07T19:05:48Z","abstract_excerpt":"The Ding-Iohara-Miki (DIM) algebra (quantum toroidal algebra of $\\widehat{gl_1}$) is related to a wide class of quantum many-particle integrable systems, a typical one being the Ruijsenaars trigonometric system with eigenfunctions that are a triad formed by the Noumi-Shiraishi power series, the Macdonald polynomials, and the Baker-Akhiezer multivariable function. Other integrable systems of this type are obtained from the Ruijsenaars system by twisting. At the same time, the Ruijsenaars Hamiltonians are directly related to the Hamiltonians of another quantum integrable system, the Cherednik DA"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.06738","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.06738/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}