{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:VLOXQ6B6SQDBVWQDPWHF3G5UWX","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":"7e8d09f2232390c89ab5ff2e09a3a8cd4761b56f524dafdafcfbe13d2c20fe14","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-03-26T20:48:38Z","title_canon_sha256":"8421f9a78a2c33253ab9fada08334bb316f2a53e9c58a56111ca8697d6982e1f"},"schema_version":"1.0","source":{"id":"1503.07890","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.07890","created_at":"2026-05-18T02:20:02Z"},{"alias_kind":"arxiv_version","alias_value":"1503.07890v2","created_at":"2026-05-18T02:20:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.07890","created_at":"2026-05-18T02:20:02Z"},{"alias_kind":"pith_short_12","alias_value":"VLOXQ6B6SQDB","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"VLOXQ6B6SQDBVWQD","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"VLOXQ6B6","created_at":"2026-05-18T12:29:44Z"}],"graph_snapshots":[{"event_id":"sha256:e84abc3b5c46f4e2b38f35a8db72f4823c4dd8be5f0053e26e02cbe249464bb9","target":"graph","created_at":"2026-05-18T02:20:02Z","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":"We classify the simple modules for the rational Cherednik algebra that are irreducible when restricted to W, in the case when W is a finite Weyl group. The classification turns out to be closely related to the cuspidal two-sided cells in the sense of Lusztig. We compute the Dirac cohomology of these modules and use the tools of Dirac theory to find nontrivial relations between the cuspidal Calogero-Moser cells and the cuspidal two-sided cells.","authors_text":"Dan Ciubotaru","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-03-26T20:48:38Z","title":"One-W-type modules for rational Cherednik algebra and cuspidal two-sided cells"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.07890","kind":"arxiv","version":2},"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:dc9410f0a78535f690bf91608df4df5c1f8bf5fe0b9ce17bb7729b3ff113b946","target":"record","created_at":"2026-05-18T02:20:02Z","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":"7e8d09f2232390c89ab5ff2e09a3a8cd4761b56f524dafdafcfbe13d2c20fe14","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-03-26T20:48:38Z","title_canon_sha256":"8421f9a78a2c33253ab9fada08334bb316f2a53e9c58a56111ca8697d6982e1f"},"schema_version":"1.0","source":{"id":"1503.07890","kind":"arxiv","version":2}},"canonical_sha256":"aadd78783e94061ada037d8e5d9bb4b5e6335083666f0580c01082a95f2e1af3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"aadd78783e94061ada037d8e5d9bb4b5e6335083666f0580c01082a95f2e1af3","first_computed_at":"2026-05-18T02:20:02.471877Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:20:02.471877Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BlvYZZWOhjmsK/A7/EHNBGR1gGb3rfWQ2u1DCUA3+76/eH/5i6T39k64XrA7RHiFzQXopzhIJUqb7yTNwLtcBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:20:02.472617Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.07890","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dc9410f0a78535f690bf91608df4df5c1f8bf5fe0b9ce17bb7729b3ff113b946","sha256:e84abc3b5c46f4e2b38f35a8db72f4823c4dd8be5f0053e26e02cbe249464bb9"],"state_sha256":"d4eb00c22510660dfe320138718fc5307f365527b0821ba02046259a08392788"}