{"paper":{"title":"Coset Vertex Operator Algebras and $\\W$-Algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Cuipo Jiang, Tomoyuki Arakawa","submitted_at":"2017-01-24T14:08:17Z","abstract_excerpt":"We give an explicit description for the weight three generator of the coset vertex operator algebra $C_{L_{\\widehat{\\sl_{n}}}(l,0)\\otimes L_{\\widehat{\\sl_{n}}}(1,0)}(L_{\\widehat{\\sl_{n}}}(l+1,0))$, for $n\\geq 2, l\\geq 1$. Furthermore, we prove that the commutant $C_{L_{\\widehat{\\sl_{3}}}(l,0)\\otimes L_{\\widehat{\\sl_{3}}}(1,0)}(L_{\\widehat{\\sl_{3}}}(l+1,0))$ is isomorphic to the $\\W$-algebra $\\W_{-3+\\frac{l+3}{l+4}}(\\sl_3)$, which confirms the conjecture for the $\\sl_3$ case that $C_{L_{\\widehat{\\frak g}}(l,0)\\otimes L_{\\widehat{\\frak g}}(1,0)}(L_{\\widehat{\\frak g}}(l+1,0))$ is isomorphic to $\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.06880","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":""},"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"}