{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2006:2HTE4LF7XO64GZXVIA2LERR5YS","short_pith_number":"pith:2HTE4LF7","schema_version":"1.0","canonical_sha256":"d1e64e2cbfbbbdc366f54034b2463dc49476471d4cc6e54ca804691c02924ea9","source":{"kind":"arxiv","id":"math/0608775","version":1},"attestation_state":"computed","paper":{"title":"Richardson elements for parabolic subgroups of classical groups in positive characteristic","license":"","headline":"","cross_cats":["math.GR"],"primary_cat":"math.RT","authors_text":"Karin Baur, Simon M. Goodwin","submitted_at":"2006-08-31T09:15:03Z","abstract_excerpt":"Let $G$ be a simple algebraic group of classical type over an algebraically closed field $k$. Let $P$ be a parabolic subgroup of $G$ and let $\\p = \\Lie P$ be the Lie algebra of $P$ with Levi decomposition $\\p = {\\l}\\oplus \\u$, where $\\u$ is the Lie algebra of the unipotent radical of $P$ and $\\l$ is a Levi complement. Thanks to a fundamental theorem of R. W. Richardson, $P$ acts on $\\u$ with an open dense orbit; this orbit is called the {\\em Richardson orbit} and its elements are called {\\em Richardson elements}. Recently, the first author gave constructions of Richardson elements in the case "},"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":"math/0608775","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.RT","submitted_at":"2006-08-31T09:15:03Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"5b6fce503b73bc8c81b1d2518cd0ec8b317fa751a2eb7825aff68d1550610741","abstract_canon_sha256":"c52e743dda839640b6f431f93e0dab8d11380f91bf3872f260a99eab6e9ce45e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:35:47.096668Z","signature_b64":"8Uq28mcUqUYfBxOT2DRiqOJX6vSa0UNVurc63cGE7JHeIIjeUrdd94Ke4n+ynYu5A0CZN6Ao5xoWesMS66RmBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d1e64e2cbfbbbdc366f54034b2463dc49476471d4cc6e54ca804691c02924ea9","last_reissued_at":"2026-05-18T04:35:47.096222Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:35:47.096222Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Richardson elements for parabolic subgroups of classical groups in positive characteristic","license":"","headline":"","cross_cats":["math.GR"],"primary_cat":"math.RT","authors_text":"Karin Baur, Simon M. Goodwin","submitted_at":"2006-08-31T09:15:03Z","abstract_excerpt":"Let $G$ be a simple algebraic group of classical type over an algebraically closed field $k$. Let $P$ be a parabolic subgroup of $G$ and let $\\p = \\Lie P$ be the Lie algebra of $P$ with Levi decomposition $\\p = {\\l}\\oplus \\u$, where $\\u$ is the Lie algebra of the unipotent radical of $P$ and $\\l$ is a Levi complement. Thanks to a fundamental theorem of R. W. Richardson, $P$ acts on $\\u$ with an open dense orbit; this orbit is called the {\\em Richardson orbit} and its elements are called {\\em Richardson elements}. Recently, the first author gave constructions of Richardson elements in the case "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0608775","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":"math/0608775","created_at":"2026-05-18T04:35:47.096288+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0608775v1","created_at":"2026-05-18T04:35:47.096288+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0608775","created_at":"2026-05-18T04:35:47.096288+00:00"},{"alias_kind":"pith_short_12","alias_value":"2HTE4LF7XO64","created_at":"2026-05-18T12:25:53.939244+00:00"},{"alias_kind":"pith_short_16","alias_value":"2HTE4LF7XO64GZXV","created_at":"2026-05-18T12:25:53.939244+00:00"},{"alias_kind":"pith_short_8","alias_value":"2HTE4LF7","created_at":"2026-05-18T12:25:53.939244+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/2HTE4LF7XO64GZXVIA2LERR5YS","json":"https://pith.science/pith/2HTE4LF7XO64GZXVIA2LERR5YS.json","graph_json":"https://pith.science/api/pith-number/2HTE4LF7XO64GZXVIA2LERR5YS/graph.json","events_json":"https://pith.science/api/pith-number/2HTE4LF7XO64GZXVIA2LERR5YS/events.json","paper":"https://pith.science/paper/2HTE4LF7"},"agent_actions":{"view_html":"https://pith.science/pith/2HTE4LF7XO64GZXVIA2LERR5YS","download_json":"https://pith.science/pith/2HTE4LF7XO64GZXVIA2LERR5YS.json","view_paper":"https://pith.science/paper/2HTE4LF7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0608775&json=true","fetch_graph":"https://pith.science/api/pith-number/2HTE4LF7XO64GZXVIA2LERR5YS/graph.json","fetch_events":"https://pith.science/api/pith-number/2HTE4LF7XO64GZXVIA2LERR5YS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2HTE4LF7XO64GZXVIA2LERR5YS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2HTE4LF7XO64GZXVIA2LERR5YS/action/storage_attestation","attest_author":"https://pith.science/pith/2HTE4LF7XO64GZXVIA2LERR5YS/action/author_attestation","sign_citation":"https://pith.science/pith/2HTE4LF7XO64GZXVIA2LERR5YS/action/citation_signature","submit_replication":"https://pith.science/pith/2HTE4LF7XO64GZXVIA2LERR5YS/action/replication_record"}},"created_at":"2026-05-18T04:35:47.096288+00:00","updated_at":"2026-05-18T04:35:47.096288+00:00"}