{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:4CLQ5FGHR7HUWN637AQEIBQCK4","short_pith_number":"pith:4CLQ5FGH","schema_version":"1.0","canonical_sha256":"e0970e94c78fcf4b37dbf820440602572f91729333994d7e9548727645f4eb7f","source":{"kind":"arxiv","id":"1009.3229","version":4},"attestation_state":"computed","paper":{"title":"Enveloping algebras of Slodowy slices and Goldie rank","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.RT","authors_text":"Alexander Premet","submitted_at":"2010-09-16T17:28:35Z","abstract_excerpt":"It is known that any primitive ideal I of U(g) whose associated variety contains a nilpotent element e in its open G-orbit admits a finite generalised Gelfand-Graev model which is a finite dimensional irreducible module over the finite W-algebra U(g,e). We prove that if V is such a model for I, then the Goldie rank of the primitive quotient U(g)/I always divides the dimension of V. For g=sl(n), we use a result of Joseph to show that the Goldie rank of U(g)/I equals the dimension of V and we show that the equality conntinues to hold outside type A provided that the Goldie field of U(g)/I is iso"},"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":"1009.3229","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2010-09-16T17:28:35Z","cross_cats_sorted":["math.RA"],"title_canon_sha256":"c12ff732ad62ef61442a335060ed1ff0594c392a82866506849830dabcb293ce","abstract_canon_sha256":"b0cb6d4ae53b6d2220146af32d9c49151d83d590e954e8db2367202a40a0b8de"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:33:17.827522Z","signature_b64":"z78jBNEYZ22ox5U5AI19v7Zz2t+MygRxKrJGT36v+ScK7OyCkly405u++GXJUtilVwZUN17e9HCZFBCq9f9ECw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e0970e94c78fcf4b37dbf820440602572f91729333994d7e9548727645f4eb7f","last_reissued_at":"2026-05-18T04:33:17.827002Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:33:17.827002Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Enveloping algebras of Slodowy slices and Goldie rank","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.RT","authors_text":"Alexander Premet","submitted_at":"2010-09-16T17:28:35Z","abstract_excerpt":"It is known that any primitive ideal I of U(g) whose associated variety contains a nilpotent element e in its open G-orbit admits a finite generalised Gelfand-Graev model which is a finite dimensional irreducible module over the finite W-algebra U(g,e). We prove that if V is such a model for I, then the Goldie rank of the primitive quotient U(g)/I always divides the dimension of V. For g=sl(n), we use a result of Joseph to show that the Goldie rank of U(g)/I equals the dimension of V and we show that the equality conntinues to hold outside type A provided that the Goldie field of U(g)/I is iso"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.3229","kind":"arxiv","version":4},"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":"1009.3229","created_at":"2026-05-18T04:33:17.827085+00:00"},{"alias_kind":"arxiv_version","alias_value":"1009.3229v4","created_at":"2026-05-18T04:33:17.827085+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.3229","created_at":"2026-05-18T04:33:17.827085+00:00"},{"alias_kind":"pith_short_12","alias_value":"4CLQ5FGHR7HU","created_at":"2026-05-18T12:26:03.138858+00:00"},{"alias_kind":"pith_short_16","alias_value":"4CLQ5FGHR7HUWN63","created_at":"2026-05-18T12:26:03.138858+00:00"},{"alias_kind":"pith_short_8","alias_value":"4CLQ5FGH","created_at":"2026-05-18T12:26:03.138858+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/4CLQ5FGHR7HUWN637AQEIBQCK4","json":"https://pith.science/pith/4CLQ5FGHR7HUWN637AQEIBQCK4.json","graph_json":"https://pith.science/api/pith-number/4CLQ5FGHR7HUWN637AQEIBQCK4/graph.json","events_json":"https://pith.science/api/pith-number/4CLQ5FGHR7HUWN637AQEIBQCK4/events.json","paper":"https://pith.science/paper/4CLQ5FGH"},"agent_actions":{"view_html":"https://pith.science/pith/4CLQ5FGHR7HUWN637AQEIBQCK4","download_json":"https://pith.science/pith/4CLQ5FGHR7HUWN637AQEIBQCK4.json","view_paper":"https://pith.science/paper/4CLQ5FGH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1009.3229&json=true","fetch_graph":"https://pith.science/api/pith-number/4CLQ5FGHR7HUWN637AQEIBQCK4/graph.json","fetch_events":"https://pith.science/api/pith-number/4CLQ5FGHR7HUWN637AQEIBQCK4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4CLQ5FGHR7HUWN637AQEIBQCK4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4CLQ5FGHR7HUWN637AQEIBQCK4/action/storage_attestation","attest_author":"https://pith.science/pith/4CLQ5FGHR7HUWN637AQEIBQCK4/action/author_attestation","sign_citation":"https://pith.science/pith/4CLQ5FGHR7HUWN637AQEIBQCK4/action/citation_signature","submit_replication":"https://pith.science/pith/4CLQ5FGHR7HUWN637AQEIBQCK4/action/replication_record"}},"created_at":"2026-05-18T04:33:17.827085+00:00","updated_at":"2026-05-18T04:33:17.827085+00:00"}