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A class of spherical homogeneous spaces containing the tori, the complete homogeneous spaces and the group $G$ (viewed as a $G\\times G$-homogeneous space) has particularly nice proterties. Namely, the pair $(G,H)$ is called a {\\it spherical pair of minimal rank} if there exists $x$ in $G/B$ such that the orbit $H.x$ of $x$ by $H$ is open in $G/B$ and the stabilizer $H_x$ of $x$ in $H$ conta"},"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":"0909.0653","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-09-03T13:50:15Z","cross_cats_sorted":[],"title_canon_sha256":"2241e13fae6e4412a510f4396b6619f5927a6f30a6865377ca4801342fa21ed0","abstract_canon_sha256":"68c2b6ca41818ef929fd73913b5e78d76f7791625938bceaa76cf23d0b732ac3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:40:57.343678Z","signature_b64":"tmslNs/lbxsh7cLSzC9tBKhPF9oYB6mbQuBG9iuH77YxsjGD4Vcmu+N/O5dMU7+dZ7AE/O3drklIknQ8cmScCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f26e10fabfb9a3b9aa7f71aa76ebe0e31daf1f1a4b275c827f963dbc1048d85a","last_reissued_at":"2026-05-18T04:40:57.342972Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:40:57.342972Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Spherical homogeneous spaces of minimal rank","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Nicolas Ressayre (I3M)","submitted_at":"2009-09-03T13:50:15Z","abstract_excerpt":"Let $G$ be a complex connected reductive algebraic group and $G/B$ denote the flag variety of $G$. A $G$-homogeneous space $G/H$ is said to be {\\it spherical} if $H$ acts on $G/B$ with finitely many orbits. A class of spherical homogeneous spaces containing the tori, the complete homogeneous spaces and the group $G$ (viewed as a $G\\times G$-homogeneous space) has particularly nice proterties. Namely, the pair $(G,H)$ is called a {\\it spherical pair of minimal rank} if there exists $x$ in $G/B$ such that the orbit $H.x$ of $x$ by $H$ is open in $G/B$ and the stabilizer $H_x$ of $x$ in $H$ conta"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0909.0653","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":"0909.0653","created_at":"2026-05-18T04:40:57.343084+00:00"},{"alias_kind":"arxiv_version","alias_value":"0909.0653v1","created_at":"2026-05-18T04:40:57.343084+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0909.0653","created_at":"2026-05-18T04:40:57.343084+00:00"},{"alias_kind":"pith_short_12","alias_value":"6JXBB6V7XGR3","created_at":"2026-05-18T12:25:58.837520+00:00"},{"alias_kind":"pith_short_16","alias_value":"6JXBB6V7XGR3TKT7","created_at":"2026-05-18T12:25:58.837520+00:00"},{"alias_kind":"pith_short_8","alias_value":"6JXBB6V7","created_at":"2026-05-18T12:25:58.837520+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/6JXBB6V7XGR3TKT7OGVHN27A4M","json":"https://pith.science/pith/6JXBB6V7XGR3TKT7OGVHN27A4M.json","graph_json":"https://pith.science/api/pith-number/6JXBB6V7XGR3TKT7OGVHN27A4M/graph.json","events_json":"https://pith.science/api/pith-number/6JXBB6V7XGR3TKT7OGVHN27A4M/events.json","paper":"https://pith.science/paper/6JXBB6V7"},"agent_actions":{"view_html":"https://pith.science/pith/6JXBB6V7XGR3TKT7OGVHN27A4M","download_json":"https://pith.science/pith/6JXBB6V7XGR3TKT7OGVHN27A4M.json","view_paper":"https://pith.science/paper/6JXBB6V7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0909.0653&json=true","fetch_graph":"https://pith.science/api/pith-number/6JXBB6V7XGR3TKT7OGVHN27A4M/graph.json","fetch_events":"https://pith.science/api/pith-number/6JXBB6V7XGR3TKT7OGVHN27A4M/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6JXBB6V7XGR3TKT7OGVHN27A4M/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6JXBB6V7XGR3TKT7OGVHN27A4M/action/storage_attestation","attest_author":"https://pith.science/pith/6JXBB6V7XGR3TKT7OGVHN27A4M/action/author_attestation","sign_citation":"https://pith.science/pith/6JXBB6V7XGR3TKT7OGVHN27A4M/action/citation_signature","submit_replication":"https://pith.science/pith/6JXBB6V7XGR3TKT7OGVHN27A4M/action/replication_record"}},"created_at":"2026-05-18T04:40:57.343084+00:00","updated_at":"2026-05-18T04:40:57.343084+00:00"}