{"paper":{"title":"Weight representations of admissible affine vertex algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.RT","authors_text":"Luis Enrique Ramirez, Tomoyuki Arakawa, Vyacheslav Futorny","submitted_at":"2016-05-24T18:38:02Z","abstract_excerpt":"For an admissible affine vertex algebra $V_k(\\mathfrak{g})$ of type $A$, we describe a new family of relaxed highest weight representations of $V_k(\\mathfrak{g})$. They are simple quotients of representations of the affine Kac-Moody algebra $\\widehat{\\mathfrak{g}}$ induced from the following $\\mathfrak{g}$-modules: 1) generic Gelfand-Tsetlin modules in the principal nilpotent orbit, in particular all such modules induced from $\\mathfrak{sl}_2$; 2) all Gelfand-Tsetlin modules in the principal nilpotent orbit which are induced from $\\mathfrak{sl}_3$; 3) all simple Gelfand-Tsetlin modules over $\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.07580","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":""},"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"}