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Then we describe G-orbits on the triple flag varieties G/P\\times G/P\\times G/P and G/P\\times G/P\\times G/B with respect to the diagonal action of G where P is a maximal parabolic subgroup of G of the shape (n,1,n) and B is a Borel subgroup. As by-products, we also describe GL_n-orbits on G/B, Q_{2n}-orbits on the full flag variety of GL_{2n} where Q_{2n} is the fixed-point subgroup in Sp_{2n} of a nonzero vector in F^{2n} and 1\\times Sp_{2n}-orbits on the full flag variety of GL_{2n+1}. In the same way, "},"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":"1011.6468","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2010-11-30T06:40:16Z","cross_cats_sorted":[],"title_canon_sha256":"009774f3b77e1c2969d530facc46f634bd67c93e0791949ed3fe3ee4a107ca43","abstract_canon_sha256":"a08d54b5c2ef4fcc97020d0b8ccb4eb15a1eaf1f1f65e211c57e0d7c157418a0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:19:34.784347Z","signature_b64":"hsPRbu9JvJEuhqmFnsx99258vOVi4ph9TPuWy5v61VNoInV2zh+Xx0PavcWEiZN7uA5ft+H4gVJG5gM90euxAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fb09674881d417d89b76e0dc1dda67096ca62c581dcda320f4785d6a7f0f8524","last_reissued_at":"2026-05-18T01:19:34.783777Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:19:34.783777Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An example of orthogonal triple flag variety of finite type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Toshihiko Matsuki","submitted_at":"2010-11-30T06:40:16Z","abstract_excerpt":"Let G be the split special orthogonal group of degree 2n+1 over a field F of char F \\ne 2. Then we describe G-orbits on the triple flag varieties G/P\\times G/P\\times G/P and G/P\\times G/P\\times G/B with respect to the diagonal action of G where P is a maximal parabolic subgroup of G of the shape (n,1,n) and B is a Borel subgroup. As by-products, we also describe GL_n-orbits on G/B, Q_{2n}-orbits on the full flag variety of GL_{2n} where Q_{2n} is the fixed-point subgroup in Sp_{2n} of a nonzero vector in F^{2n} and 1\\times Sp_{2n}-orbits on the full flag variety of GL_{2n+1}. In the same way, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.6468","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":"1011.6468","created_at":"2026-05-18T01:19:34.783841+00:00"},{"alias_kind":"arxiv_version","alias_value":"1011.6468v2","created_at":"2026-05-18T01:19:34.783841+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.6468","created_at":"2026-05-18T01:19:34.783841+00:00"},{"alias_kind":"pith_short_12","alias_value":"7MEWOSEB2QL5","created_at":"2026-05-18T12:26:05.355336+00:00"},{"alias_kind":"pith_short_16","alias_value":"7MEWOSEB2QL5RG3W","created_at":"2026-05-18T12:26:05.355336+00:00"},{"alias_kind":"pith_short_8","alias_value":"7MEWOSEB","created_at":"2026-05-18T12:26:05.355336+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/7MEWOSEB2QL5RG3W4DOB3WTHBF","json":"https://pith.science/pith/7MEWOSEB2QL5RG3W4DOB3WTHBF.json","graph_json":"https://pith.science/api/pith-number/7MEWOSEB2QL5RG3W4DOB3WTHBF/graph.json","events_json":"https://pith.science/api/pith-number/7MEWOSEB2QL5RG3W4DOB3WTHBF/events.json","paper":"https://pith.science/paper/7MEWOSEB"},"agent_actions":{"view_html":"https://pith.science/pith/7MEWOSEB2QL5RG3W4DOB3WTHBF","download_json":"https://pith.science/pith/7MEWOSEB2QL5RG3W4DOB3WTHBF.json","view_paper":"https://pith.science/paper/7MEWOSEB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1011.6468&json=true","fetch_graph":"https://pith.science/api/pith-number/7MEWOSEB2QL5RG3W4DOB3WTHBF/graph.json","fetch_events":"https://pith.science/api/pith-number/7MEWOSEB2QL5RG3W4DOB3WTHBF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7MEWOSEB2QL5RG3W4DOB3WTHBF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7MEWOSEB2QL5RG3W4DOB3WTHBF/action/storage_attestation","attest_author":"https://pith.science/pith/7MEWOSEB2QL5RG3W4DOB3WTHBF/action/author_attestation","sign_citation":"https://pith.science/pith/7MEWOSEB2QL5RG3W4DOB3WTHBF/action/citation_signature","submit_replication":"https://pith.science/pith/7MEWOSEB2QL5RG3W4DOB3WTHBF/action/replication_record"}},"created_at":"2026-05-18T01:19:34.783841+00:00","updated_at":"2026-05-18T01:19:34.783841+00:00"}