{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:T674QZ6NWZTBSHHVVCUBXA3ML5","short_pith_number":"pith:T674QZ6N","schema_version":"1.0","canonical_sha256":"9fbfc867cdb666191cf5a8a81b836c5f68177ef4b1970a5638ca1bec09fca117","source":{"kind":"arxiv","id":"1707.01196","version":1},"attestation_state":"computed","paper":{"title":"Temperley-Lieb at roots of unity, a fusion category and the Jones quotient","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"G.I. Lehrer, K. Iohara, R.B. Zhang","submitted_at":"2017-07-05T02:11:43Z","abstract_excerpt":"When the parameter $q$ is a root of unity, the Temperley-Lieb algebra $TL_n(q)$ is non-semisimple for almost all $n$. In this work, using cellular methods, we give explicit generating functions for the dimensions of all the simple $TL_n(q)$-modules. Jones showed that if the order $|q^2|=\\ell$ there is a canonical symmetric bilinear form on $TL_n(q)$, whose radical $R_n(q)$ is generated by a certain idempotent $E_\\ell\\in TL_{\\ell-1}(q)\\subseteq TL_n(q)$, which is now referred to as the Jones-Wenzl idempotent, for which an explicit formula was subsequently given by Graham and Lehrer. Although th"},"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":"1707.01196","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-07-05T02:11:43Z","cross_cats_sorted":[],"title_canon_sha256":"000c39ef520972dd8635c105147f4ace24c76f356550d8fc8cf9dbc206ade88d","abstract_canon_sha256":"5fa3b3917b0675a70e14c5ad19ae27ed23e824e5361b7d7ccaa2b0630353502c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:40:53.464228Z","signature_b64":"vbgX3TbP+lt2f9W5AFoOB5A9rY8xa5DxXkOuh2YX+VOal+aPqozy2TEv2mdUj4gF0aJmJfzdBMpjybsqsk+dDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9fbfc867cdb666191cf5a8a81b836c5f68177ef4b1970a5638ca1bec09fca117","last_reissued_at":"2026-05-18T00:40:53.463617Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:40:53.463617Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Temperley-Lieb at roots of unity, a fusion category and the Jones quotient","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"G.I. Lehrer, K. Iohara, R.B. Zhang","submitted_at":"2017-07-05T02:11:43Z","abstract_excerpt":"When the parameter $q$ is a root of unity, the Temperley-Lieb algebra $TL_n(q)$ is non-semisimple for almost all $n$. In this work, using cellular methods, we give explicit generating functions for the dimensions of all the simple $TL_n(q)$-modules. Jones showed that if the order $|q^2|=\\ell$ there is a canonical symmetric bilinear form on $TL_n(q)$, whose radical $R_n(q)$ is generated by a certain idempotent $E_\\ell\\in TL_{\\ell-1}(q)\\subseteq TL_n(q)$, which is now referred to as the Jones-Wenzl idempotent, for which an explicit formula was subsequently given by Graham and Lehrer. Although th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.01196","kind":"arxiv","version":1},"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":"1707.01196","created_at":"2026-05-18T00:40:53.463710+00:00"},{"alias_kind":"arxiv_version","alias_value":"1707.01196v1","created_at":"2026-05-18T00:40:53.463710+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.01196","created_at":"2026-05-18T00:40:53.463710+00:00"},{"alias_kind":"pith_short_12","alias_value":"T674QZ6NWZTB","created_at":"2026-05-18T12:31:43.269735+00:00"},{"alias_kind":"pith_short_16","alias_value":"T674QZ6NWZTBSHHV","created_at":"2026-05-18T12:31:43.269735+00:00"},{"alias_kind":"pith_short_8","alias_value":"T674QZ6N","created_at":"2026-05-18T12:31:43.269735+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/T674QZ6NWZTBSHHVVCUBXA3ML5","json":"https://pith.science/pith/T674QZ6NWZTBSHHVVCUBXA3ML5.json","graph_json":"https://pith.science/api/pith-number/T674QZ6NWZTBSHHVVCUBXA3ML5/graph.json","events_json":"https://pith.science/api/pith-number/T674QZ6NWZTBSHHVVCUBXA3ML5/events.json","paper":"https://pith.science/paper/T674QZ6N"},"agent_actions":{"view_html":"https://pith.science/pith/T674QZ6NWZTBSHHVVCUBXA3ML5","download_json":"https://pith.science/pith/T674QZ6NWZTBSHHVVCUBXA3ML5.json","view_paper":"https://pith.science/paper/T674QZ6N","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1707.01196&json=true","fetch_graph":"https://pith.science/api/pith-number/T674QZ6NWZTBSHHVVCUBXA3ML5/graph.json","fetch_events":"https://pith.science/api/pith-number/T674QZ6NWZTBSHHVVCUBXA3ML5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/T674QZ6NWZTBSHHVVCUBXA3ML5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/T674QZ6NWZTBSHHVVCUBXA3ML5/action/storage_attestation","attest_author":"https://pith.science/pith/T674QZ6NWZTBSHHVVCUBXA3ML5/action/author_attestation","sign_citation":"https://pith.science/pith/T674QZ6NWZTBSHHVVCUBXA3ML5/action/citation_signature","submit_replication":"https://pith.science/pith/T674QZ6NWZTBSHHVVCUBXA3ML5/action/replication_record"}},"created_at":"2026-05-18T00:40:53.463710+00:00","updated_at":"2026-05-18T00:40:53.463710+00:00"}