{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2005:HH3U4NTDDUBT66A6JWCVGFIGKL","short_pith_number":"pith:HH3U4NTD","schema_version":"1.0","canonical_sha256":"39f74e36631d033f781e4d8553150652efa39416446e046f8321b28f87741bdf","source":{"kind":"arxiv","id":"math/0506403","version":4},"attestation_state":"computed","paper":{"title":"The quantum $\\mathfrak{sl}(n,\\mathbb{C})$ representation theory and its applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.GT","authors_text":"Dongseok Kim, Myeong-Ju Jeong","submitted_at":"2005-06-20T15:41:51Z","abstract_excerpt":"In this paper, we study the quantum $\\mathfrak{sl}(n)$ representation category using the web space. Specially, we extend $\\mathfrak{sl}(n)$ web space for $n\\ge 4$ as generalized Temperley-Lieb algebras. As an application of our study, we find that the HOMFLY polynomial $P_n(q)$ specialized to a one variable polynomial can be computed by a linear expansion with respect to a presentation of the quantum representation category of $\\mathfrak{sl}(n)$. Moreover, we correct the false conjecture \\cite{PS:superiod} given by Chbili, which addresses the relation between some link polynomials of a periodi"},"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":"math/0506403","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2005-06-20T15:41:51Z","cross_cats_sorted":["math.QA"],"title_canon_sha256":"28a5128063979100e393fbee67eb8c2748e50d687431105ec6804b76aad8df2d","abstract_canon_sha256":"4cfa509525bf1b48743f654a0a66ba8f18df582bd7b5e1ec4bd3992421eae775"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:41:02.750394Z","signature_b64":"hC5908EgJbpupkjuIr/tFTnTIVWXU4T2OjKs+vayWIBDhfjD/GbsnnG0zLK897VT3gQmjb00IqsadRexFKP3CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"39f74e36631d033f781e4d8553150652efa39416446e046f8321b28f87741bdf","last_reissued_at":"2026-05-18T03:41:02.749920Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:41:02.749920Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The quantum $\\mathfrak{sl}(n,\\mathbb{C})$ representation theory and its applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.GT","authors_text":"Dongseok Kim, Myeong-Ju Jeong","submitted_at":"2005-06-20T15:41:51Z","abstract_excerpt":"In this paper, we study the quantum $\\mathfrak{sl}(n)$ representation category using the web space. Specially, we extend $\\mathfrak{sl}(n)$ web space for $n\\ge 4$ as generalized Temperley-Lieb algebras. As an application of our study, we find that the HOMFLY polynomial $P_n(q)$ specialized to a one variable polynomial can be computed by a linear expansion with respect to a presentation of the quantum representation category of $\\mathfrak{sl}(n)$. Moreover, we correct the false conjecture \\cite{PS:superiod} given by Chbili, which addresses the relation between some link polynomials of a periodi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0506403","kind":"arxiv","version":4},"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":"math/0506403","created_at":"2026-05-18T03:41:02.749990+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0506403v4","created_at":"2026-05-18T03:41:02.749990+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0506403","created_at":"2026-05-18T03:41:02.749990+00:00"},{"alias_kind":"pith_short_12","alias_value":"HH3U4NTDDUBT","created_at":"2026-05-18T12:25:53.335082+00:00"},{"alias_kind":"pith_short_16","alias_value":"HH3U4NTDDUBT66A6","created_at":"2026-05-18T12:25:53.335082+00:00"},{"alias_kind":"pith_short_8","alias_value":"HH3U4NTD","created_at":"2026-05-18T12:25:53.335082+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/HH3U4NTDDUBT66A6JWCVGFIGKL","json":"https://pith.science/pith/HH3U4NTDDUBT66A6JWCVGFIGKL.json","graph_json":"https://pith.science/api/pith-number/HH3U4NTDDUBT66A6JWCVGFIGKL/graph.json","events_json":"https://pith.science/api/pith-number/HH3U4NTDDUBT66A6JWCVGFIGKL/events.json","paper":"https://pith.science/paper/HH3U4NTD"},"agent_actions":{"view_html":"https://pith.science/pith/HH3U4NTDDUBT66A6JWCVGFIGKL","download_json":"https://pith.science/pith/HH3U4NTDDUBT66A6JWCVGFIGKL.json","view_paper":"https://pith.science/paper/HH3U4NTD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0506403&json=true","fetch_graph":"https://pith.science/api/pith-number/HH3U4NTDDUBT66A6JWCVGFIGKL/graph.json","fetch_events":"https://pith.science/api/pith-number/HH3U4NTDDUBT66A6JWCVGFIGKL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HH3U4NTDDUBT66A6JWCVGFIGKL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HH3U4NTDDUBT66A6JWCVGFIGKL/action/storage_attestation","attest_author":"https://pith.science/pith/HH3U4NTDDUBT66A6JWCVGFIGKL/action/author_attestation","sign_citation":"https://pith.science/pith/HH3U4NTDDUBT66A6JWCVGFIGKL/action/citation_signature","submit_replication":"https://pith.science/pith/HH3U4NTDDUBT66A6JWCVGFIGKL/action/replication_record"}},"created_at":"2026-05-18T03:41:02.749990+00:00","updated_at":"2026-05-18T03:41:02.749990+00:00"}