{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:6JWRUNI2BLJ4CHID7KLUI5I6QQ","short_pith_number":"pith:6JWRUNI2","schema_version":"1.0","canonical_sha256":"f26d1a351a0ad3c11d03fa9744751e840846346bb94da5f1e01081984adec8a8","source":{"kind":"arxiv","id":"1110.5672","version":2},"attestation_state":"computed","paper":{"title":"Kazhdan--Lusztig cells and the Frobenius--Schur indicator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Meinolf Geck","submitted_at":"2011-10-25T21:47:00Z","abstract_excerpt":"Let $W$ be a finite Coxeter group. It is well-known that the number of involutions in $W$ is equal to the sum of the degrees of the irreducible characters of $W$. Following a suggestion of Lusztig, we show that this equality is compatible with the decomposition of $W$ into Kazhdan--Lusztig cells. The proof uses a generalisation of the Frobenius--Schur indicator to symmetric algebras, which may be of independent interest."},"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":"1110.5672","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-10-25T21:47:00Z","cross_cats_sorted":[],"title_canon_sha256":"8f9b5e163d3c2881ba1a1a2ba3396ffef6dd55b7ace537ed6c1570f797f64ecb","abstract_canon_sha256":"d44a3ff7e495aa8b35b8b8239fb8d7b127e6fac5732b0402226925f57e47043a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:06:07.512079Z","signature_b64":"fUSXV92woZo+cgMfyR9LUJnOJ+KCwDWFLDsA1ZqbrB3Okx/goAPlnBMwGap516s426HNCAw2Cu7ZX6rV42qMCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f26d1a351a0ad3c11d03fa9744751e840846346bb94da5f1e01081984adec8a8","last_reissued_at":"2026-05-18T04:06:07.511586Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:06:07.511586Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Kazhdan--Lusztig cells and the Frobenius--Schur indicator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Meinolf Geck","submitted_at":"2011-10-25T21:47:00Z","abstract_excerpt":"Let $W$ be a finite Coxeter group. It is well-known that the number of involutions in $W$ is equal to the sum of the degrees of the irreducible characters of $W$. Following a suggestion of Lusztig, we show that this equality is compatible with the decomposition of $W$ into Kazhdan--Lusztig cells. The proof uses a generalisation of the Frobenius--Schur indicator to symmetric algebras, which may be of independent interest."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.5672","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":"1110.5672","created_at":"2026-05-18T04:06:07.511658+00:00"},{"alias_kind":"arxiv_version","alias_value":"1110.5672v2","created_at":"2026-05-18T04:06:07.511658+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.5672","created_at":"2026-05-18T04:06:07.511658+00:00"},{"alias_kind":"pith_short_12","alias_value":"6JWRUNI2BLJ4","created_at":"2026-05-18T12:26:22.705136+00:00"},{"alias_kind":"pith_short_16","alias_value":"6JWRUNI2BLJ4CHID","created_at":"2026-05-18T12:26:22.705136+00:00"},{"alias_kind":"pith_short_8","alias_value":"6JWRUNI2","created_at":"2026-05-18T12:26:22.705136+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/6JWRUNI2BLJ4CHID7KLUI5I6QQ","json":"https://pith.science/pith/6JWRUNI2BLJ4CHID7KLUI5I6QQ.json","graph_json":"https://pith.science/api/pith-number/6JWRUNI2BLJ4CHID7KLUI5I6QQ/graph.json","events_json":"https://pith.science/api/pith-number/6JWRUNI2BLJ4CHID7KLUI5I6QQ/events.json","paper":"https://pith.science/paper/6JWRUNI2"},"agent_actions":{"view_html":"https://pith.science/pith/6JWRUNI2BLJ4CHID7KLUI5I6QQ","download_json":"https://pith.science/pith/6JWRUNI2BLJ4CHID7KLUI5I6QQ.json","view_paper":"https://pith.science/paper/6JWRUNI2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1110.5672&json=true","fetch_graph":"https://pith.science/api/pith-number/6JWRUNI2BLJ4CHID7KLUI5I6QQ/graph.json","fetch_events":"https://pith.science/api/pith-number/6JWRUNI2BLJ4CHID7KLUI5I6QQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6JWRUNI2BLJ4CHID7KLUI5I6QQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6JWRUNI2BLJ4CHID7KLUI5I6QQ/action/storage_attestation","attest_author":"https://pith.science/pith/6JWRUNI2BLJ4CHID7KLUI5I6QQ/action/author_attestation","sign_citation":"https://pith.science/pith/6JWRUNI2BLJ4CHID7KLUI5I6QQ/action/citation_signature","submit_replication":"https://pith.science/pith/6JWRUNI2BLJ4CHID7KLUI5I6QQ/action/replication_record"}},"created_at":"2026-05-18T04:06:07.511658+00:00","updated_at":"2026-05-18T04:06:07.511658+00:00"}