{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:O5MVGDN3EL763T2QYHS3V2RG7B","short_pith_number":"pith:O5MVGDN3","schema_version":"1.0","canonical_sha256":"7759530dbb22ffedcf50c1e5baea26f87876dbc6e5d69f5f7ee9fff59e67a361","source":{"kind":"arxiv","id":"1207.6315","version":2},"attestation_state":"computed","paper":{"title":"Localization of cohomological induction","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Yoshiki Oshima","submitted_at":"2012-07-26T16:16:46Z","abstract_excerpt":"We give a geometric realization of cohomologically induced (g,K)-modules. Let (h,L) be a subpair of (g,K). The cohomological induction is an algebraic construction of (g,K)-modules from a (h,L)-module V. For a real semisimple Lie group, the duality theorem by Hecht, Milicic, Schmid, and Wolf relates (g,K)-modules cohomologically induced from a Borel subalgebra with D-modules on the flag variety of g. In this article we extend the theorem for more general pairs (g,K) and (h,L). We consider the tensor product of a D-module and a certain module associated with V, and prove that its sheaf cohomolo"},"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":"1207.6315","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-07-26T16:16:46Z","cross_cats_sorted":[],"title_canon_sha256":"1b0ef806c723d79e6f636deecf5d4bfe6e6c826820958e2e97f4d991a2b22d99","abstract_canon_sha256":"6e62a9791e2b49f78a38a0151874cf3edb35949857ea396d5154c6b3b79fea3c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:21:20.770767Z","signature_b64":"udX1nwRu3Umo/pbCOO1txBLUjsZvpx+TYjAb7osJugBXiFHf+fkfb8RnJ9u4SVpe8wJNgfDDHXw6XeHRCNWLDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7759530dbb22ffedcf50c1e5baea26f87876dbc6e5d69f5f7ee9fff59e67a361","last_reissued_at":"2026-05-18T03:21:20.770293Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:21:20.770293Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Localization of cohomological induction","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Yoshiki Oshima","submitted_at":"2012-07-26T16:16:46Z","abstract_excerpt":"We give a geometric realization of cohomologically induced (g,K)-modules. Let (h,L) be a subpair of (g,K). The cohomological induction is an algebraic construction of (g,K)-modules from a (h,L)-module V. For a real semisimple Lie group, the duality theorem by Hecht, Milicic, Schmid, and Wolf relates (g,K)-modules cohomologically induced from a Borel subalgebra with D-modules on the flag variety of g. In this article we extend the theorem for more general pairs (g,K) and (h,L). We consider the tensor product of a D-module and a certain module associated with V, and prove that its sheaf cohomolo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.6315","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":""},"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":"1207.6315","created_at":"2026-05-18T03:21:20.770376+00:00"},{"alias_kind":"arxiv_version","alias_value":"1207.6315v2","created_at":"2026-05-18T03:21:20.770376+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.6315","created_at":"2026-05-18T03:21:20.770376+00:00"},{"alias_kind":"pith_short_12","alias_value":"O5MVGDN3EL76","created_at":"2026-05-18T12:27:16.716162+00:00"},{"alias_kind":"pith_short_16","alias_value":"O5MVGDN3EL763T2Q","created_at":"2026-05-18T12:27:16.716162+00:00"},{"alias_kind":"pith_short_8","alias_value":"O5MVGDN3","created_at":"2026-05-18T12:27:16.716162+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/O5MVGDN3EL763T2QYHS3V2RG7B","json":"https://pith.science/pith/O5MVGDN3EL763T2QYHS3V2RG7B.json","graph_json":"https://pith.science/api/pith-number/O5MVGDN3EL763T2QYHS3V2RG7B/graph.json","events_json":"https://pith.science/api/pith-number/O5MVGDN3EL763T2QYHS3V2RG7B/events.json","paper":"https://pith.science/paper/O5MVGDN3"},"agent_actions":{"view_html":"https://pith.science/pith/O5MVGDN3EL763T2QYHS3V2RG7B","download_json":"https://pith.science/pith/O5MVGDN3EL763T2QYHS3V2RG7B.json","view_paper":"https://pith.science/paper/O5MVGDN3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1207.6315&json=true","fetch_graph":"https://pith.science/api/pith-number/O5MVGDN3EL763T2QYHS3V2RG7B/graph.json","fetch_events":"https://pith.science/api/pith-number/O5MVGDN3EL763T2QYHS3V2RG7B/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/O5MVGDN3EL763T2QYHS3V2RG7B/action/timestamp_anchor","attest_storage":"https://pith.science/pith/O5MVGDN3EL763T2QYHS3V2RG7B/action/storage_attestation","attest_author":"https://pith.science/pith/O5MVGDN3EL763T2QYHS3V2RG7B/action/author_attestation","sign_citation":"https://pith.science/pith/O5MVGDN3EL763T2QYHS3V2RG7B/action/citation_signature","submit_replication":"https://pith.science/pith/O5MVGDN3EL763T2QYHS3V2RG7B/action/replication_record"}},"created_at":"2026-05-18T03:21:20.770376+00:00","updated_at":"2026-05-18T03:21:20.770376+00:00"}