{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2020:BE5EDM6FIOADT5DAB7SZKD5K6L","short_pith_number":"pith:BE5EDM6F","schema_version":"1.0","canonical_sha256":"093a41b3c5438039f4600fe5950faaf2fb343c057cda65350509686edf251328","source":{"kind":"arxiv","id":"2011.10021","version":1},"attestation_state":"computed","paper":{"title":"Bershadsky-Polyakov vertex algebras at positive integer levels and duality","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Ana Kontrec, Drazen Adamovic","submitted_at":"2020-11-19T18:39:13Z","abstract_excerpt":"We study the simple Bershadsky-Polyakov algebra $\\mathcal W_k = \\mathcal{W}_k(sl_3,f_{\\theta})$ at positive integer levels and classify their irreducible modules. In this way we confirm the conjecture from arXiv:1910.13781. Next, we study the case $k=1$. We discover that this vertex algebra has a Kazama-Suzuki-type dual isomorphic to the simple afine vertex superalgebra $L_{k'} (osp(1 \\vert 2))$ for $k'=-5/4$. Using the free-field realization of $L_{k'} (osp(1 \\vert 2))$ from arXiv:1711.11342, we get a free-field realization of $\\mathcal W_k$ and their highest weight modules. In a sequel, we p"},"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":"2011.10021","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.QA","submitted_at":"2020-11-19T18:39:13Z","cross_cats_sorted":[],"title_canon_sha256":"e1ba578a6426dcb222732b02a63089331a3f48b14bbd1a0614ebb82be961ac94","abstract_canon_sha256":"1f361b422efc9b734c32f08145414536039da013affd7071ca52170924b71823"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:53:03.872918Z","signature_b64":"rB+ZGuKU07jNjVHNO4vuLXkzuvvCT/iqKezafAbVDyJ926ekxtPfJ0FyJQE8iiDCBqRIDRlRxWh1kbX69TkMBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"093a41b3c5438039f4600fe5950faaf2fb343c057cda65350509686edf251328","last_reissued_at":"2026-07-05T01:53:03.872527Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:53:03.872527Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Bershadsky-Polyakov vertex algebras at positive integer levels and duality","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Ana Kontrec, Drazen Adamovic","submitted_at":"2020-11-19T18:39:13Z","abstract_excerpt":"We study the simple Bershadsky-Polyakov algebra $\\mathcal W_k = \\mathcal{W}_k(sl_3,f_{\\theta})$ at positive integer levels and classify their irreducible modules. In this way we confirm the conjecture from arXiv:1910.13781. Next, we study the case $k=1$. We discover that this vertex algebra has a Kazama-Suzuki-type dual isomorphic to the simple afine vertex superalgebra $L_{k'} (osp(1 \\vert 2))$ for $k'=-5/4$. Using the free-field realization of $L_{k'} (osp(1 \\vert 2))$ from arXiv:1711.11342, we get a free-field realization of $\\mathcal W_k$ and their highest weight modules. In a sequel, we p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2011.10021","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2011.10021/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2011.10021","created_at":"2026-07-05T01:53:03.872592+00:00"},{"alias_kind":"arxiv_version","alias_value":"2011.10021v1","created_at":"2026-07-05T01:53:03.872592+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2011.10021","created_at":"2026-07-05T01:53:03.872592+00:00"},{"alias_kind":"pith_short_12","alias_value":"BE5EDM6FIOAD","created_at":"2026-07-05T01:53:03.872592+00:00"},{"alias_kind":"pith_short_16","alias_value":"BE5EDM6FIOADT5DA","created_at":"2026-07-05T01:53:03.872592+00:00"},{"alias_kind":"pith_short_8","alias_value":"BE5EDM6F","created_at":"2026-07-05T01:53:03.872592+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2411.08406","citing_title":"On Kazama-Suzuki Duality between $\\mathcal{W}_k(\\mathfrak{sl}_4, f_{\\rm sub})$ and $N=2$ Superconformal Vertex Algebra","ref_index":5,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/BE5EDM6FIOADT5DAB7SZKD5K6L","json":"https://pith.science/pith/BE5EDM6FIOADT5DAB7SZKD5K6L.json","graph_json":"https://pith.science/api/pith-number/BE5EDM6FIOADT5DAB7SZKD5K6L/graph.json","events_json":"https://pith.science/api/pith-number/BE5EDM6FIOADT5DAB7SZKD5K6L/events.json","paper":"https://pith.science/paper/BE5EDM6F"},"agent_actions":{"view_html":"https://pith.science/pith/BE5EDM6FIOADT5DAB7SZKD5K6L","download_json":"https://pith.science/pith/BE5EDM6FIOADT5DAB7SZKD5K6L.json","view_paper":"https://pith.science/paper/BE5EDM6F","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2011.10021&json=true","fetch_graph":"https://pith.science/api/pith-number/BE5EDM6FIOADT5DAB7SZKD5K6L/graph.json","fetch_events":"https://pith.science/api/pith-number/BE5EDM6FIOADT5DAB7SZKD5K6L/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BE5EDM6FIOADT5DAB7SZKD5K6L/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BE5EDM6FIOADT5DAB7SZKD5K6L/action/storage_attestation","attest_author":"https://pith.science/pith/BE5EDM6FIOADT5DAB7SZKD5K6L/action/author_attestation","sign_citation":"https://pith.science/pith/BE5EDM6FIOADT5DAB7SZKD5K6L/action/citation_signature","submit_replication":"https://pith.science/pith/BE5EDM6FIOADT5DAB7SZKD5K6L/action/replication_record"}},"created_at":"2026-07-05T01:53:03.872592+00:00","updated_at":"2026-07-05T01:53:03.872592+00:00"}