{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:ZTP4BXL446BZLL2ZYOP4HV2HCE","short_pith_number":"pith:ZTP4BXL4","schema_version":"1.0","canonical_sha256":"ccdfc0dd7ce78395af59c39fc3d7471113107dcdc9ce37b1ecaaf1dd31f134bd","source":{"kind":"arxiv","id":"1205.3762","version":2},"attestation_state":"computed","paper":{"title":"Ordering Lusztig's families in type $B_n$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Lacrimioara Iancu, Meinolf Geck","submitted_at":"2012-05-16T19:03:13Z","abstract_excerpt":"Let $W$ be a finite Coxeter group and $L$ be a weight function on $W$ in the sense of Lusztig. We have recently introduced a pre-order relation $\\preceq_L$ on the set of irreducible characters of $W$ which extends Lusztig's definition of \"families\" and which, conjecturally, corresponds to the ordering given by Kazhdan--Lusztig cells. Here, we give an explicit description of $\\preceq_L$ for $W$ of type $B_n$ and any $L$. (All other cases are known from previous work.) This crucially relies on some new combinatorial constructions around Lusztig's \"symbols\". Combined with previous work, we deduce"},"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":"1205.3762","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-05-16T19:03:13Z","cross_cats_sorted":[],"title_canon_sha256":"1800ae3c0c4a729c584380c87ea0078ae2a198ff8437540adfb5b4c73e4e611b","abstract_canon_sha256":"dca22d5e97c68a1fa120e7770753d7251ac7752b4fc65b29bda29511aef135d4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:55:02.415662Z","signature_b64":"ja1dubKasf45b85AZ2IV2UV12t+OXfcbAZUfWDZ0WcK5aGYPYfsi70LIOTrOfWBN03x8GIqyY5ztU6i+Clb6DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ccdfc0dd7ce78395af59c39fc3d7471113107dcdc9ce37b1ecaaf1dd31f134bd","last_reissued_at":"2026-05-18T03:55:02.415052Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:55:02.415052Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Ordering Lusztig's families in type $B_n$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Lacrimioara Iancu, Meinolf Geck","submitted_at":"2012-05-16T19:03:13Z","abstract_excerpt":"Let $W$ be a finite Coxeter group and $L$ be a weight function on $W$ in the sense of Lusztig. We have recently introduced a pre-order relation $\\preceq_L$ on the set of irreducible characters of $W$ which extends Lusztig's definition of \"families\" and which, conjecturally, corresponds to the ordering given by Kazhdan--Lusztig cells. Here, we give an explicit description of $\\preceq_L$ for $W$ of type $B_n$ and any $L$. (All other cases are known from previous work.) This crucially relies on some new combinatorial constructions around Lusztig's \"symbols\". Combined with previous work, we deduce"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.3762","kind":"arxiv","version":2},"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":"1205.3762","created_at":"2026-05-18T03:55:02.415144+00:00"},{"alias_kind":"arxiv_version","alias_value":"1205.3762v2","created_at":"2026-05-18T03:55:02.415144+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.3762","created_at":"2026-05-18T03:55:02.415144+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZTP4BXL446BZ","created_at":"2026-05-18T12:27:30.460161+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZTP4BXL446BZLL2Z","created_at":"2026-05-18T12:27:30.460161+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZTP4BXL4","created_at":"2026-05-18T12:27:30.460161+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/ZTP4BXL446BZLL2ZYOP4HV2HCE","json":"https://pith.science/pith/ZTP4BXL446BZLL2ZYOP4HV2HCE.json","graph_json":"https://pith.science/api/pith-number/ZTP4BXL446BZLL2ZYOP4HV2HCE/graph.json","events_json":"https://pith.science/api/pith-number/ZTP4BXL446BZLL2ZYOP4HV2HCE/events.json","paper":"https://pith.science/paper/ZTP4BXL4"},"agent_actions":{"view_html":"https://pith.science/pith/ZTP4BXL446BZLL2ZYOP4HV2HCE","download_json":"https://pith.science/pith/ZTP4BXL446BZLL2ZYOP4HV2HCE.json","view_paper":"https://pith.science/paper/ZTP4BXL4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1205.3762&json=true","fetch_graph":"https://pith.science/api/pith-number/ZTP4BXL446BZLL2ZYOP4HV2HCE/graph.json","fetch_events":"https://pith.science/api/pith-number/ZTP4BXL446BZLL2ZYOP4HV2HCE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZTP4BXL446BZLL2ZYOP4HV2HCE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZTP4BXL446BZLL2ZYOP4HV2HCE/action/storage_attestation","attest_author":"https://pith.science/pith/ZTP4BXL446BZLL2ZYOP4HV2HCE/action/author_attestation","sign_citation":"https://pith.science/pith/ZTP4BXL446BZLL2ZYOP4HV2HCE/action/citation_signature","submit_replication":"https://pith.science/pith/ZTP4BXL446BZLL2ZYOP4HV2HCE/action/replication_record"}},"created_at":"2026-05-18T03:55:02.415144+00:00","updated_at":"2026-05-18T03:55:02.415144+00:00"}