{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:2V72V57E5LU3VDJDND4VV2O2PO","short_pith_number":"pith:2V72V57E","schema_version":"1.0","canonical_sha256":"d57faaf7e4eae9ba8d2368f95ae9da7b958c5358d7bbf13dfc2452483fb8c35e","source":{"kind":"arxiv","id":"1707.05092","version":1},"attestation_state":"computed","paper":{"title":"Conformally covariant differential operators for the diagonal action of O(p, q) on real quadrics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Jean-Louis Clerc","submitted_at":"2017-07-17T11:06:52Z","abstract_excerpt":"Let $X=G/P$ be a real projective quadric, where $G=O(p,q)$ and $P$ is a parabolic subgroup of $G$. Let $\\left(\\pi_{\\lambda,\\epsilon}, \\mathcal{H}_{\\lambda,\\epsilon}\\right)_{ (\\lambda,\\epsilon)\\in \\mathbb {C}\\times \\{\\pm\\}}$ be the family of (smooth) representations of $G$ induced from the characters of $P$. For $(\\lambda, \\epsilon), (\\mu, \\eta)\\in \\mathbb{C} \\times \\{\\pm\\}$,  a differential operator $\\mathbf{D}_{(\\lambda,\\epsilon), (\\mu,\\eta)}^{reg}$ on $X\\times X$, acting $G$-covariantly from  $\\mathcal{H}_{\\lambda,\\epsilon} \\otimes \\mathcal{H}_{\\mu, \\eta}$ into $\\mathcal{H}_{\\lambda+1,-\\epsi"},"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":"1707.05092","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-07-17T11:06:52Z","cross_cats_sorted":[],"title_canon_sha256":"c879b30f90096b3b4a13f3e5372f98fe501225419c73525d9d7b4432dcf823c9","abstract_canon_sha256":"ad41edc3ad2acc82059cfb7313d9ec3a03d921c39614cca11cba157c3a80be3c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:40:11.413749Z","signature_b64":"qq3dM2XMjVIKcAo2VGf7YBn74OksDiVR3R5bLF1koNSkuFg0b2Ygwbce54OfZdu/VxJjKTWp7r3+VbB7CFdZDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d57faaf7e4eae9ba8d2368f95ae9da7b958c5358d7bbf13dfc2452483fb8c35e","last_reissued_at":"2026-05-18T00:40:11.413275Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:40:11.413275Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Conformally covariant differential operators for the diagonal action of O(p, q) on real quadrics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Jean-Louis Clerc","submitted_at":"2017-07-17T11:06:52Z","abstract_excerpt":"Let $X=G/P$ be a real projective quadric, where $G=O(p,q)$ and $P$ is a parabolic subgroup of $G$. Let $\\left(\\pi_{\\lambda,\\epsilon}, \\mathcal{H}_{\\lambda,\\epsilon}\\right)_{ (\\lambda,\\epsilon)\\in \\mathbb {C}\\times \\{\\pm\\}}$ be the family of (smooth) representations of $G$ induced from the characters of $P$. For $(\\lambda, \\epsilon), (\\mu, \\eta)\\in \\mathbb{C} \\times \\{\\pm\\}$,  a differential operator $\\mathbf{D}_{(\\lambda,\\epsilon), (\\mu,\\eta)}^{reg}$ on $X\\times X$, acting $G$-covariantly from  $\\mathcal{H}_{\\lambda,\\epsilon} \\otimes \\mathcal{H}_{\\mu, \\eta}$ into $\\mathcal{H}_{\\lambda+1,-\\epsi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.05092","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":"1707.05092","created_at":"2026-05-18T00:40:11.413349+00:00"},{"alias_kind":"arxiv_version","alias_value":"1707.05092v1","created_at":"2026-05-18T00:40:11.413349+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.05092","created_at":"2026-05-18T00:40:11.413349+00:00"},{"alias_kind":"pith_short_12","alias_value":"2V72V57E5LU3","created_at":"2026-05-18T12:30:55.937587+00:00"},{"alias_kind":"pith_short_16","alias_value":"2V72V57E5LU3VDJD","created_at":"2026-05-18T12:30:55.937587+00:00"},{"alias_kind":"pith_short_8","alias_value":"2V72V57E","created_at":"2026-05-18T12:30:55.937587+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/2V72V57E5LU3VDJDND4VV2O2PO","json":"https://pith.science/pith/2V72V57E5LU3VDJDND4VV2O2PO.json","graph_json":"https://pith.science/api/pith-number/2V72V57E5LU3VDJDND4VV2O2PO/graph.json","events_json":"https://pith.science/api/pith-number/2V72V57E5LU3VDJDND4VV2O2PO/events.json","paper":"https://pith.science/paper/2V72V57E"},"agent_actions":{"view_html":"https://pith.science/pith/2V72V57E5LU3VDJDND4VV2O2PO","download_json":"https://pith.science/pith/2V72V57E5LU3VDJDND4VV2O2PO.json","view_paper":"https://pith.science/paper/2V72V57E","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1707.05092&json=true","fetch_graph":"https://pith.science/api/pith-number/2V72V57E5LU3VDJDND4VV2O2PO/graph.json","fetch_events":"https://pith.science/api/pith-number/2V72V57E5LU3VDJDND4VV2O2PO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2V72V57E5LU3VDJDND4VV2O2PO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2V72V57E5LU3VDJDND4VV2O2PO/action/storage_attestation","attest_author":"https://pith.science/pith/2V72V57E5LU3VDJDND4VV2O2PO/action/author_attestation","sign_citation":"https://pith.science/pith/2V72V57E5LU3VDJDND4VV2O2PO/action/citation_signature","submit_replication":"https://pith.science/pith/2V72V57E5LU3VDJDND4VV2O2PO/action/replication_record"}},"created_at":"2026-05-18T00:40:11.413349+00:00","updated_at":"2026-05-18T00:40:11.413349+00:00"}