{"paper":{"title":"Vertex algebras related to regular representations of $SL_2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Antun Milas, Drazen Adamovic","submitted_at":"2025-02-03T19:10:45Z","abstract_excerpt":"We construct a family of potentially quasi-lisse (non-rational) vertex algebras, denoted by $\\mathcal{C}_p$, $p \\geq 2$, which are closely related to the vertex algebra of chiral differential operators on $SL(2)$ at level $-2+\\frac{1}{p}$. We prove that for $p = 3$, there is an isomorphism between $\\mathcal{C}_3$ and the affine vertex algebra $L_{-5/3}(\\mathfrak{g}_2)$ from Deligne's series. Moreover, we also establish isomorphisms between $\\mathcal{C}_4$ and $\\mathcal{C}_5$ and certain affine ${W}$-algebras of types $F_4$ and $E_8$, respectively. In this way, we resolve the problem of decompo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.01766","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/2502.01766/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"}