{"paper":{"title":"Representation theory of $L_k\\left(\\mathfrak{osp}(1 | 2)\\right)$ from vertex tensor categories and Jacobi forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.RT"],"primary_cat":"math.QA","authors_text":"Jesse Frohlich, Shashank Kanade, Thomas Creutzig","submitted_at":"2017-06-01T10:19:45Z","abstract_excerpt":"The purpose of this work is to illustrate in a family of interesting examples how to study the representation theory of vertex operator superalgebras by combining the theory of vertex algebra extensions and modular forms.\n  Let $L_k\\left(\\mathfrak{osp}(1 | 2)\\right)$ be the simple affine vertex operator superalgebra of $\\mathfrak{osp}(1|2)$ at an admissible level $k$. We use a Jacobi form decomposition to see that this is a vertex operator superalgebra extension of $L_k(\\mathfrak{sl}_2)\\otimes \\text{Vir}(p, (p+p')/2)$ where $k+3/2=p/(2p')$ and $\\text{Vir}(u, v)$ denotes the regular Virasoro ve"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.00242","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"}