{"paper":{"title":"Cosets of the $\\mathcal{W}^k(\\mathfrak{sl}_4, f_{\\text{subreg}})$-algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.RT","authors_text":"Andrew R. Linshaw, Thomas Creutzig","submitted_at":"2017-11-29T21:19:15Z","abstract_excerpt":"Let $\\mathcal {W}^k(\\mathfrak{sl}_4, f_{\\text {subreg}})$ be the universal $\\mathcal{W}$-algebra associated to $\\mathfrak{sl}_4$ with its subregular nilpotent element, and let $\\mathcal {W}_k(\\mathfrak{sl}_4, f_{\\text {subreg}})$ be its simple quotient. There is a Heisenberg subalgebra $\\mathcal{H}$, and we denote by $\\mathcal{C}^k$ the coset $\\text{Com}(\\mathcal{H}, \\mathcal {W}^k(\\mathfrak{sl}_4, f_{\\text {subreg}}))$, and by $\\mathcal{C}_k$ its simple quotient. We show that for $k=-4+(m+4)/3$ where $m$ is an integer greater than $2$ and $m+1$ is coprime to $3$, $\\mathcal{C}_k$ is isomorphic"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.11109","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/1711.11109/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"}