{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2021:CRNQTIXAAHHL4OPMU2LVYQBGUM","short_pith_number":"pith:CRNQTIXA","schema_version":"1.0","canonical_sha256":"145b09a2e001cebe39eca6975c4026a323075c3d6f1058b0bdb736bf77e04bf5","source":{"kind":"arxiv","id":"2103.02985","version":2},"attestation_state":"computed","paper":{"title":"On the representation theory of the vertex algebra $L_{-5/2}(sl(4))$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.QA","authors_text":"Drazen Adamovic, Ivana Vukorepa, Ozren Perse","submitted_at":"2021-03-04T12:18:36Z","abstract_excerpt":"We study the representation theory of non-admissible simple affine vertex algebra $L_{-5/2} (sl(4))$. We determine an explicit formula for the singular vector of conformal weight four in the universal affine vertex algebra $V^{-5/2} (sl(4))$, and show that it generates the maximal ideal in $V^{-5/2} (sl(4))$. We classify irreducible $L_{-5/2} (sl(4))$--modules in the category ${\\mathcal O}$, and determine the fusion rules between irreducible modules in the category of ordinary modules $KL_{-5/2}$. It turns out that this fusion algebra is isomorphic to the fusion algebra of $KL_{-1}$. We also 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":"2103.02985","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2021-03-04T12:18:36Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"5bda6eb709dfa4ccc85113889c2abddf58d1b0e52b780a4141d5ebb9ac2a8b43","abstract_canon_sha256":"2b39a5aa17c81a5f009940a7e284c78a9c1b30d6684c8a0ce38c52b8b0f10c25"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:36:53.228705Z","signature_b64":"6LycoTScrVPse+tF1Ibdwo9BbxB6YKP5z9GbJYMLl0WMOnvF4p2E6P89mA37NrLcXT61wBs3mkZpiV4SsdJvCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"145b09a2e001cebe39eca6975c4026a323075c3d6f1058b0bdb736bf77e04bf5","last_reissued_at":"2026-07-05T03:36:53.228213Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:36:53.228213Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the representation theory of the vertex algebra $L_{-5/2}(sl(4))$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.QA","authors_text":"Drazen Adamovic, Ivana Vukorepa, Ozren Perse","submitted_at":"2021-03-04T12:18:36Z","abstract_excerpt":"We study the representation theory of non-admissible simple affine vertex algebra $L_{-5/2} (sl(4))$. We determine an explicit formula for the singular vector of conformal weight four in the universal affine vertex algebra $V^{-5/2} (sl(4))$, and show that it generates the maximal ideal in $V^{-5/2} (sl(4))$. We classify irreducible $L_{-5/2} (sl(4))$--modules in the category ${\\mathcal O}$, and determine the fusion rules between irreducible modules in the category of ordinary modules $KL_{-5/2}$. It turns out that this fusion algebra is isomorphic to the fusion algebra of $KL_{-1}$. We also p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2103.02985","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2103.02985/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":"2103.02985","created_at":"2026-07-05T03:36:53.228277+00:00"},{"alias_kind":"arxiv_version","alias_value":"2103.02985v2","created_at":"2026-07-05T03:36:53.228277+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2103.02985","created_at":"2026-07-05T03:36:53.228277+00:00"},{"alias_kind":"pith_short_12","alias_value":"CRNQTIXAAHHL","created_at":"2026-07-05T03:36:53.228277+00:00"},{"alias_kind":"pith_short_16","alias_value":"CRNQTIXAAHHL4OPM","created_at":"2026-07-05T03:36:53.228277+00:00"},{"alias_kind":"pith_short_8","alias_value":"CRNQTIXA","created_at":"2026-07-05T03:36:53.228277+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":9,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/CRNQTIXAAHHL4OPMU2LVYQBGUM","json":"https://pith.science/pith/CRNQTIXAAHHL4OPMU2LVYQBGUM.json","graph_json":"https://pith.science/api/pith-number/CRNQTIXAAHHL4OPMU2LVYQBGUM/graph.json","events_json":"https://pith.science/api/pith-number/CRNQTIXAAHHL4OPMU2LVYQBGUM/events.json","paper":"https://pith.science/paper/CRNQTIXA"},"agent_actions":{"view_html":"https://pith.science/pith/CRNQTIXAAHHL4OPMU2LVYQBGUM","download_json":"https://pith.science/pith/CRNQTIXAAHHL4OPMU2LVYQBGUM.json","view_paper":"https://pith.science/paper/CRNQTIXA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2103.02985&json=true","fetch_graph":"https://pith.science/api/pith-number/CRNQTIXAAHHL4OPMU2LVYQBGUM/graph.json","fetch_events":"https://pith.science/api/pith-number/CRNQTIXAAHHL4OPMU2LVYQBGUM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CRNQTIXAAHHL4OPMU2LVYQBGUM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CRNQTIXAAHHL4OPMU2LVYQBGUM/action/storage_attestation","attest_author":"https://pith.science/pith/CRNQTIXAAHHL4OPMU2LVYQBGUM/action/author_attestation","sign_citation":"https://pith.science/pith/CRNQTIXAAHHL4OPMU2LVYQBGUM/action/citation_signature","submit_replication":"https://pith.science/pith/CRNQTIXAAHHL4OPMU2LVYQBGUM/action/replication_record"}},"created_at":"2026-07-05T03:36:53.228277+00:00","updated_at":"2026-07-05T03:36:53.228277+00:00"}