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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1706.00242","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2017-06-01T10:19:45Z","cross_cats_sorted":["math-ph","math.MP","math.RT"],"title_canon_sha256":"2b5a8c9f9a5efbfee541147fe15d8a94865ad3b7a2d1946f9a83d984643bde35","abstract_canon_sha256":"b393e9132fd0fee424321319fb33102094a8021098c0473310959f39067c4caf"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:43:14.637445Z","signature_b64":"fiBGyUVDS1kesQiEJEXfeOJlInNx5g+StPQcWcDIDLkfc16OWoXt0qLXh9vxxWrBkXLtYboPS8sXypVJ9Fd0DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6a5487c3a11b7f444f825c58fc0189792af592c8bdfb8486b034db5498e14d35","last_reissued_at":"2026-05-18T00:43:14.636883Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:43:14.636883Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $k$. 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