{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:XCSTRPWHI2B2X7SICBMJ7QNFED","short_pith_number":"pith:XCSTRPWH","schema_version":"1.0","canonical_sha256":"b8a538bec74683abfe4810589fc1a520cb4c149edfb269bc5fbe4735da3523c1","source":{"kind":"arxiv","id":"1204.1118","version":1},"attestation_state":"computed","paper":{"title":"Closed orbits on partial flag varieties and double flag variety of finite type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.RT","authors_text":"Hiroyuki Ochiai, Kenji Taniguchi, Kensuke Kondo, Kyo Nishiyama","submitted_at":"2012-04-05T04:26:53Z","abstract_excerpt":"Let $ G $ be a connected reductive algebraic group over $ \\C $. We denote by $ K = (G^{\\theta})_{0} $ the identity component of the fixed points of an involutive automorphism $ \\theta $ of $ G $. The pair $ (G, K) $ is called a symmetric pair.\n  Let $Q$ be a parabolic subgroup of $K$. We want to find a pair of parabolic subgroups $P_{1}$, $P_{2}$ of $G$ such that (i) $P_{1} \\cap P_{2} = Q$ and (ii) $P_{1} P_{2}$ is dense in $G$. The main result of this article states that, for a simple group $G$, we can find such a pair if and only if $(G, K)$ is a Hermitian symmetric pair.\n  The conditions (i"},"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":"1204.1118","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-04-05T04:26:53Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"ff1bc75ea26d8fce9ac1df5b2761dca741215745a14d57b10ed787b586345417","abstract_canon_sha256":"966890518cf930857d528ad8e73367f8a4fb60240343a2173822c3db263cfb9b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:58:36.347478Z","signature_b64":"XD9/8iQrk6kb/hU64rAjBuAyVqpRkexS8DQHFn6ppmQLzU1WZGcHjQM+Xb5hXqIf998jFRSczUzZNsjRgi11Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b8a538bec74683abfe4810589fc1a520cb4c149edfb269bc5fbe4735da3523c1","last_reissued_at":"2026-05-18T03:58:36.346925Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:58:36.346925Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Closed orbits on partial flag varieties and double flag variety of finite type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.RT","authors_text":"Hiroyuki Ochiai, Kenji Taniguchi, Kensuke Kondo, Kyo Nishiyama","submitted_at":"2012-04-05T04:26:53Z","abstract_excerpt":"Let $ G $ be a connected reductive algebraic group over $ \\C $. We denote by $ K = (G^{\\theta})_{0} $ the identity component of the fixed points of an involutive automorphism $ \\theta $ of $ G $. The pair $ (G, K) $ is called a symmetric pair.\n  Let $Q$ be a parabolic subgroup of $K$. We want to find a pair of parabolic subgroups $P_{1}$, $P_{2}$ of $G$ such that (i) $P_{1} \\cap P_{2} = Q$ and (ii) $P_{1} P_{2}$ is dense in $G$. The main result of this article states that, for a simple group $G$, we can find such a pair if and only if $(G, K)$ is a Hermitian symmetric pair.\n  The conditions (i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.1118","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":"1204.1118","created_at":"2026-05-18T03:58:36.347003+00:00"},{"alias_kind":"arxiv_version","alias_value":"1204.1118v1","created_at":"2026-05-18T03:58:36.347003+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.1118","created_at":"2026-05-18T03:58:36.347003+00:00"},{"alias_kind":"pith_short_12","alias_value":"XCSTRPWHI2B2","created_at":"2026-05-18T12:27:27.928770+00:00"},{"alias_kind":"pith_short_16","alias_value":"XCSTRPWHI2B2X7SI","created_at":"2026-05-18T12:27:27.928770+00:00"},{"alias_kind":"pith_short_8","alias_value":"XCSTRPWH","created_at":"2026-05-18T12:27:27.928770+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/XCSTRPWHI2B2X7SICBMJ7QNFED","json":"https://pith.science/pith/XCSTRPWHI2B2X7SICBMJ7QNFED.json","graph_json":"https://pith.science/api/pith-number/XCSTRPWHI2B2X7SICBMJ7QNFED/graph.json","events_json":"https://pith.science/api/pith-number/XCSTRPWHI2B2X7SICBMJ7QNFED/events.json","paper":"https://pith.science/paper/XCSTRPWH"},"agent_actions":{"view_html":"https://pith.science/pith/XCSTRPWHI2B2X7SICBMJ7QNFED","download_json":"https://pith.science/pith/XCSTRPWHI2B2X7SICBMJ7QNFED.json","view_paper":"https://pith.science/paper/XCSTRPWH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1204.1118&json=true","fetch_graph":"https://pith.science/api/pith-number/XCSTRPWHI2B2X7SICBMJ7QNFED/graph.json","fetch_events":"https://pith.science/api/pith-number/XCSTRPWHI2B2X7SICBMJ7QNFED/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XCSTRPWHI2B2X7SICBMJ7QNFED/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XCSTRPWHI2B2X7SICBMJ7QNFED/action/storage_attestation","attest_author":"https://pith.science/pith/XCSTRPWHI2B2X7SICBMJ7QNFED/action/author_attestation","sign_citation":"https://pith.science/pith/XCSTRPWHI2B2X7SICBMJ7QNFED/action/citation_signature","submit_replication":"https://pith.science/pith/XCSTRPWHI2B2X7SICBMJ7QNFED/action/replication_record"}},"created_at":"2026-05-18T03:58:36.347003+00:00","updated_at":"2026-05-18T03:58:36.347003+00:00"}