{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:5I7L566EYZGF45NORWE67O2QAJ","short_pith_number":"pith:5I7L566E","schema_version":"1.0","canonical_sha256":"ea3ebefbc4c64c5e75ae8d89efbb500254f39b8a600961cdf4b5ce538fdd3adb","source":{"kind":"arxiv","id":"1603.06705","version":1},"attestation_state":"computed","paper":{"title":"Determinant Formula for Parabolic Verma Modules of Lie Superalgebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"math.RT","authors_text":"Masahito Yamazaki, Yoshiki Oshima","submitted_at":"2016-03-22T08:36:23Z","abstract_excerpt":"We prove a determinant formula for a parabolic Verma module of a Lie superalgebra, previously conjectured by the second author. Our determinant formula generalizes the previous results of Jantzen for a parabolic Verma module of a (non-super) Lie algebra, and of Kac concerning a (non-parabolic) Verma module for a Lie superalgebra. The resulting formula is expected to have a variety of applications in the study of higher-dimensional supersymmetric conformal field theories. We also discuss irreducibility criteria for the Verma module."},"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":"1603.06705","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-03-22T08:36:23Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"04f2c1672c2ddb85d859fb849812e3bc1c61ff9ab9e018fc41ab6836fe1147e8","abstract_canon_sha256":"a3a9e625d323ff00f3f75d217aabeade5d2382d4efe8672df326232d5750af8a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:28:27.328973Z","signature_b64":"i4EW+nUVj4F3+UOXxNUqu/oCv9UH6yoLm+XlX5X8+SpjqprtKFpK4Zhy2RcsklX3QB3r5kBeDIP2XZfUP9ELBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ea3ebefbc4c64c5e75ae8d89efbb500254f39b8a600961cdf4b5ce538fdd3adb","last_reissued_at":"2026-05-18T00:28:27.328331Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:28:27.328331Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Determinant Formula for Parabolic Verma Modules of Lie Superalgebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"math.RT","authors_text":"Masahito Yamazaki, Yoshiki Oshima","submitted_at":"2016-03-22T08:36:23Z","abstract_excerpt":"We prove a determinant formula for a parabolic Verma module of a Lie superalgebra, previously conjectured by the second author. Our determinant formula generalizes the previous results of Jantzen for a parabolic Verma module of a (non-super) Lie algebra, and of Kac concerning a (non-parabolic) Verma module for a Lie superalgebra. The resulting formula is expected to have a variety of applications in the study of higher-dimensional supersymmetric conformal field theories. We also discuss irreducibility criteria for the Verma module."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.06705","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1603.06705","created_at":"2026-05-18T00:28:27.328426+00:00"},{"alias_kind":"arxiv_version","alias_value":"1603.06705v1","created_at":"2026-05-18T00:28:27.328426+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.06705","created_at":"2026-05-18T00:28:27.328426+00:00"},{"alias_kind":"pith_short_12","alias_value":"5I7L566EYZGF","created_at":"2026-05-18T12:30:01.593930+00:00"},{"alias_kind":"pith_short_16","alias_value":"5I7L566EYZGF45NO","created_at":"2026-05-18T12:30:01.593930+00:00"},{"alias_kind":"pith_short_8","alias_value":"5I7L566E","created_at":"2026-05-18T12:30:01.593930+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/5I7L566EYZGF45NORWE67O2QAJ","json":"https://pith.science/pith/5I7L566EYZGF45NORWE67O2QAJ.json","graph_json":"https://pith.science/api/pith-number/5I7L566EYZGF45NORWE67O2QAJ/graph.json","events_json":"https://pith.science/api/pith-number/5I7L566EYZGF45NORWE67O2QAJ/events.json","paper":"https://pith.science/paper/5I7L566E"},"agent_actions":{"view_html":"https://pith.science/pith/5I7L566EYZGF45NORWE67O2QAJ","download_json":"https://pith.science/pith/5I7L566EYZGF45NORWE67O2QAJ.json","view_paper":"https://pith.science/paper/5I7L566E","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1603.06705&json=true","fetch_graph":"https://pith.science/api/pith-number/5I7L566EYZGF45NORWE67O2QAJ/graph.json","fetch_events":"https://pith.science/api/pith-number/5I7L566EYZGF45NORWE67O2QAJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5I7L566EYZGF45NORWE67O2QAJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5I7L566EYZGF45NORWE67O2QAJ/action/storage_attestation","attest_author":"https://pith.science/pith/5I7L566EYZGF45NORWE67O2QAJ/action/author_attestation","sign_citation":"https://pith.science/pith/5I7L566EYZGF45NORWE67O2QAJ/action/citation_signature","submit_replication":"https://pith.science/pith/5I7L566EYZGF45NORWE67O2QAJ/action/replication_record"}},"created_at":"2026-05-18T00:28:27.328426+00:00","updated_at":"2026-05-18T00:28:27.328426+00:00"}