{"paper":{"title":"A $(q,t)$-deformation of the 2d Toda integrable hierarchy","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["hep-th","math.MP","math.QA","nlin.SI"],"primary_cat":"math-ph","authors_text":"Alexandr Garbali, Jean-Emile Bourgine","submitted_at":"2023-08-31T09:28:09Z","abstract_excerpt":"A $(q,t)$-deformation of the 2d Toda integrable hierarchy is introduced by enhancing the underlying symmetry algebra $\\mathfrak{gl}(\\infty)\\simeq \\text{q-W}_{1+\\infty}$ to the quantum toroidal $\\mathfrak{gl}(1)$ algebra. The difference-differential equations of the hierarchy are obtained from the expansion of $(q,t)$-bilinear identities, and two equations refining the 2d Toda equation are found in this way. The derivation of the bilinear identities follows from the isomorphism between the Fock representation of level $(2,0)$ of the quantum toroidal $\\mathfrak{gl}(1)$ algebra and the tensor pro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2308.16583","kind":"arxiv","version":2},"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/2308.16583/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"}