{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:MYI2HL6NEE5PKURSZBX26L7JQQ","short_pith_number":"pith:MYI2HL6N","schema_version":"1.0","canonical_sha256":"6611a3afcd213af55232c86faf2fe9843bbf406745faa0b8f43df3b020668d45","source":{"kind":"arxiv","id":"0906.3881","version":3},"attestation_state":"computed","paper":{"title":"Sheets of Symmetric Lie Algebras and Slodowy Slices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.RT","authors_text":"Michael Bulois","submitted_at":"2009-06-21T17:31:43Z","abstract_excerpt":"Let T be an involution of the finite dimensional complex reductive Lie algebra g and g=k+p be the associated Cartan decomposition. Denote by K the adjoint group of k.\n  The K-module p is the union of the subsets p^{(m)}={x | dim K.x =m}, indexed by integers m, and the K-sheets of (g,T) are the irreducible components of the p^{(m)}. The sheets can be, in turn, written as a union of so-called Jordan K-classes.\n  We introduce conditions in order to describe the sheets and Jordan K-classes in terms of Slodowy slices. When g is of classical type, the K-sheets are shown to be smooth; if g=gl_N a com"},"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":"0906.3881","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2009-06-21T17:31:43Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"e0cd457e2891de7509b509d7467194cdf3bafb3b139d680c3aa70d05a270af0b","abstract_canon_sha256":"b14d383f063879c271d47da1b5eac36f794be4f45b52275fe443334a5bfb849e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:34:55.504580Z","signature_b64":"67htzMw+fQnXXenRU93bZBXqMOmHcmqEZaW15WdSvywCuX6+3EJzwYeVtyeDpGA1v6WTS6pBwIP2m7d3tPl7CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6611a3afcd213af55232c86faf2fe9843bbf406745faa0b8f43df3b020668d45","last_reissued_at":"2026-05-18T04:34:55.504175Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:34:55.504175Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Sheets of Symmetric Lie Algebras and Slodowy Slices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.RT","authors_text":"Michael Bulois","submitted_at":"2009-06-21T17:31:43Z","abstract_excerpt":"Let T be an involution of the finite dimensional complex reductive Lie algebra g and g=k+p be the associated Cartan decomposition. Denote by K the adjoint group of k.\n  The K-module p is the union of the subsets p^{(m)}={x | dim K.x =m}, indexed by integers m, and the K-sheets of (g,T) are the irreducible components of the p^{(m)}. The sheets can be, in turn, written as a union of so-called Jordan K-classes.\n  We introduce conditions in order to describe the sheets and Jordan K-classes in terms of Slodowy slices. When g is of classical type, the K-sheets are shown to be smooth; if g=gl_N a com"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0906.3881","kind":"arxiv","version":3},"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":"0906.3881","created_at":"2026-05-18T04:34:55.504231+00:00"},{"alias_kind":"arxiv_version","alias_value":"0906.3881v3","created_at":"2026-05-18T04:34:55.504231+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0906.3881","created_at":"2026-05-18T04:34:55.504231+00:00"},{"alias_kind":"pith_short_12","alias_value":"MYI2HL6NEE5P","created_at":"2026-05-18T12:26:00.592388+00:00"},{"alias_kind":"pith_short_16","alias_value":"MYI2HL6NEE5PKURS","created_at":"2026-05-18T12:26:00.592388+00:00"},{"alias_kind":"pith_short_8","alias_value":"MYI2HL6N","created_at":"2026-05-18T12:26:00.592388+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/MYI2HL6NEE5PKURSZBX26L7JQQ","json":"https://pith.science/pith/MYI2HL6NEE5PKURSZBX26L7JQQ.json","graph_json":"https://pith.science/api/pith-number/MYI2HL6NEE5PKURSZBX26L7JQQ/graph.json","events_json":"https://pith.science/api/pith-number/MYI2HL6NEE5PKURSZBX26L7JQQ/events.json","paper":"https://pith.science/paper/MYI2HL6N"},"agent_actions":{"view_html":"https://pith.science/pith/MYI2HL6NEE5PKURSZBX26L7JQQ","download_json":"https://pith.science/pith/MYI2HL6NEE5PKURSZBX26L7JQQ.json","view_paper":"https://pith.science/paper/MYI2HL6N","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0906.3881&json=true","fetch_graph":"https://pith.science/api/pith-number/MYI2HL6NEE5PKURSZBX26L7JQQ/graph.json","fetch_events":"https://pith.science/api/pith-number/MYI2HL6NEE5PKURSZBX26L7JQQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MYI2HL6NEE5PKURSZBX26L7JQQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MYI2HL6NEE5PKURSZBX26L7JQQ/action/storage_attestation","attest_author":"https://pith.science/pith/MYI2HL6NEE5PKURSZBX26L7JQQ/action/author_attestation","sign_citation":"https://pith.science/pith/MYI2HL6NEE5PKURSZBX26L7JQQ/action/citation_signature","submit_replication":"https://pith.science/pith/MYI2HL6NEE5PKURSZBX26L7JQQ/action/replication_record"}},"created_at":"2026-05-18T04:34:55.504231+00:00","updated_at":"2026-05-18T04:34:55.504231+00:00"}