{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:AGYHOB3HHGXUP5ASFZYHT5FCVI","short_pith_number":"pith:AGYHOB3H","schema_version":"1.0","canonical_sha256":"01b077076739af47f4122e7079f4a2aa015097190f55120aea3884894a81ec84","source":{"kind":"arxiv","id":"1509.06008","version":1},"attestation_state":"computed","paper":{"title":"B-orbits of square zero in nilradical of the symplectic algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Anna Melnikov, Nurit Barnea","submitted_at":"2015-09-20T12:48:21Z","abstract_excerpt":"Let $SP_n(\\mathbb{C})$ be the symplectic group and $\\mathfrak{sp}_n(\\mathbb{C})$ its Lie algebra. Let $B$ be a Borel subgroup of $SP_n(\\mathbb{C} )$, $\\mathfrak{b}={\\rm Lie}(B)$ and $\\mathfrak n$ its nilradical. Let $\\mathcal X$ be a subvariety of elements of square 0 in $\\mathfrak n.$ $B$ acts adjointly on $\\mathcal X$. In this paper we describe topology of orbits $\\mathcal X/B$ in terms of symmetric link patterns.\n  Further we apply this description to the computations of the closures of orbital varieties of nilpotency order 2 and to their intersections. In particular we show that all the in"},"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":"1509.06008","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-09-20T12:48:21Z","cross_cats_sorted":[],"title_canon_sha256":"dc7c8dae0d2a2495849fb0c182e49a332baa7a8e6f3d3e71886f2f55a0293940","abstract_canon_sha256":"974d2babf9b57652005910ac4658700ca29e18454933e07a36394467a74bfaf0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:32:36.105508Z","signature_b64":"G8FId1CD+vA87Hb5tCNwa8PcMKDJYrpxtZePkWHGjIHmFlx26thWqr7//Sl93zvwdlxcD2mb5a7btT0gyfImAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"01b077076739af47f4122e7079f4a2aa015097190f55120aea3884894a81ec84","last_reissued_at":"2026-05-18T01:32:36.104800Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:32:36.104800Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"B-orbits of square zero in nilradical of the symplectic algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Anna Melnikov, Nurit Barnea","submitted_at":"2015-09-20T12:48:21Z","abstract_excerpt":"Let $SP_n(\\mathbb{C})$ be the symplectic group and $\\mathfrak{sp}_n(\\mathbb{C})$ its Lie algebra. Let $B$ be a Borel subgroup of $SP_n(\\mathbb{C} )$, $\\mathfrak{b}={\\rm Lie}(B)$ and $\\mathfrak n$ its nilradical. Let $\\mathcal X$ be a subvariety of elements of square 0 in $\\mathfrak n.$ $B$ acts adjointly on $\\mathcal X$. In this paper we describe topology of orbits $\\mathcal X/B$ in terms of symmetric link patterns.\n  Further we apply this description to the computations of the closures of orbital varieties of nilpotency order 2 and to their intersections. In particular we show that all the in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.06008","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":"1509.06008","created_at":"2026-05-18T01:32:36.104898+00:00"},{"alias_kind":"arxiv_version","alias_value":"1509.06008v1","created_at":"2026-05-18T01:32:36.104898+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.06008","created_at":"2026-05-18T01:32:36.104898+00:00"},{"alias_kind":"pith_short_12","alias_value":"AGYHOB3HHGXU","created_at":"2026-05-18T12:29:10.953037+00:00"},{"alias_kind":"pith_short_16","alias_value":"AGYHOB3HHGXUP5AS","created_at":"2026-05-18T12:29:10.953037+00:00"},{"alias_kind":"pith_short_8","alias_value":"AGYHOB3H","created_at":"2026-05-18T12:29:10.953037+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/AGYHOB3HHGXUP5ASFZYHT5FCVI","json":"https://pith.science/pith/AGYHOB3HHGXUP5ASFZYHT5FCVI.json","graph_json":"https://pith.science/api/pith-number/AGYHOB3HHGXUP5ASFZYHT5FCVI/graph.json","events_json":"https://pith.science/api/pith-number/AGYHOB3HHGXUP5ASFZYHT5FCVI/events.json","paper":"https://pith.science/paper/AGYHOB3H"},"agent_actions":{"view_html":"https://pith.science/pith/AGYHOB3HHGXUP5ASFZYHT5FCVI","download_json":"https://pith.science/pith/AGYHOB3HHGXUP5ASFZYHT5FCVI.json","view_paper":"https://pith.science/paper/AGYHOB3H","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1509.06008&json=true","fetch_graph":"https://pith.science/api/pith-number/AGYHOB3HHGXUP5ASFZYHT5FCVI/graph.json","fetch_events":"https://pith.science/api/pith-number/AGYHOB3HHGXUP5ASFZYHT5FCVI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AGYHOB3HHGXUP5ASFZYHT5FCVI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AGYHOB3HHGXUP5ASFZYHT5FCVI/action/storage_attestation","attest_author":"https://pith.science/pith/AGYHOB3HHGXUP5ASFZYHT5FCVI/action/author_attestation","sign_citation":"https://pith.science/pith/AGYHOB3HHGXUP5ASFZYHT5FCVI/action/citation_signature","submit_replication":"https://pith.science/pith/AGYHOB3HHGXUP5ASFZYHT5FCVI/action/replication_record"}},"created_at":"2026-05-18T01:32:36.104898+00:00","updated_at":"2026-05-18T01:32:36.104898+00:00"}