{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:4CLQ5FGHR7HUWN637AQEIBQCK4","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"b0cb6d4ae53b6d2220146af32d9c49151d83d590e954e8db2367202a40a0b8de","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2010-09-16T17:28:35Z","title_canon_sha256":"c12ff732ad62ef61442a335060ed1ff0594c392a82866506849830dabcb293ce"},"schema_version":"1.0","source":{"id":"1009.3229","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.3229","created_at":"2026-05-18T04:33:17Z"},{"alias_kind":"arxiv_version","alias_value":"1009.3229v4","created_at":"2026-05-18T04:33:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.3229","created_at":"2026-05-18T04:33:17Z"},{"alias_kind":"pith_short_12","alias_value":"4CLQ5FGHR7HU","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"4CLQ5FGHR7HUWN63","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"4CLQ5FGH","created_at":"2026-05-18T12:26:03Z"}],"graph_snapshots":[{"event_id":"sha256:2d04be3702cd01d4f8f741584f5c5b8a750bf4f9785fc97f4a44dc852bcbda6c","target":"graph","created_at":"2026-05-18T04:33:17Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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","authors_text":"Alexander Premet","cross_cats":["math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2010-09-16T17:28:35Z","title":"Enveloping algebras of Slodowy slices and Goldie rank"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.3229","kind":"arxiv","version":4},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:14291ceadfba697a85ae70ac5d66e2abc55bd4f1b58cb7ed213591c22247a7af","target":"record","created_at":"2026-05-18T04:33:17Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"b0cb6d4ae53b6d2220146af32d9c49151d83d590e954e8db2367202a40a0b8de","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2010-09-16T17:28:35Z","title_canon_sha256":"c12ff732ad62ef61442a335060ed1ff0594c392a82866506849830dabcb293ce"},"schema_version":"1.0","source":{"id":"1009.3229","kind":"arxiv","version":4}},"canonical_sha256":"e0970e94c78fcf4b37dbf820440602572f91729333994d7e9548727645f4eb7f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e0970e94c78fcf4b37dbf820440602572f91729333994d7e9548727645f4eb7f","first_computed_at":"2026-05-18T04:33:17.827002Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:33:17.827002Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"z78jBNEYZ22ox5U5AI19v7Zz2t+MygRxKrJGT36v+ScK7OyCkly405u++GXJUtilVwZUN17e9HCZFBCq9f9ECw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:33:17.827522Z","signed_message":"canonical_sha256_bytes"},"source_id":"1009.3229","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:14291ceadfba697a85ae70ac5d66e2abc55bd4f1b58cb7ed213591c22247a7af","sha256:2d04be3702cd01d4f8f741584f5c5b8a750bf4f9785fc97f4a44dc852bcbda6c"],"state_sha256":"08ffcd2986ec128506e04bf081ea6b2b0e2c5a2a683be9d952bd1007918f1795"}