{"paper":{"title":"Deformations of $\\mathcal W$ algebras via quantum toroidal algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.QA","authors_text":"B. Feigin, E. Mukhin, I. Vilkoviskiy, M. Jimbo","submitted_at":"2020-03-09T16:17:55Z","abstract_excerpt":"The deformed $\\mathcal W$ algebras of type $\\textsf{A}$ have a uniform description in terms of the quantum toroidal $\\mathfrak{gl}_1$ algebra $\\mathcal E$. We introduce a comodule algebra $\\mathcal K$ over $\\mathcal E$ which gives a uniform construction of basic deformed $\\mathcal W$ currents and screening operators in types $\\textsf{B},\\textsf{C},\\textsf{D}$ including twisted and supersymmetric cases. We show that a completion of algebra $\\mathcal K$ contains three commutative subalgebras. In particular, it allows us to obtain a commutative family of integrals of motion associated with affine"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2003.04234","kind":"arxiv","version":3},"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/2003.04234/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"}