{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:RVGXVJMELTMDM36AJHGKXQEEEW","short_pith_number":"pith:RVGXVJME","canonical_record":{"source":{"id":"1104.5101","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.QA","submitted_at":"2011-04-27T09:56:59Z","cross_cats_sorted":[],"title_canon_sha256":"4085810574c2890c707292bc9e1ea3dff200db7da4c00667f7319ab052a4eb22","abstract_canon_sha256":"4d0d82ac154a731e02727ae0f2269ccea300633e54a52c7cde287a7adb0bdc18"},"schema_version":"1.0"},"canonical_sha256":"8d4d7aa5845cd8366fc049ccabc08425b5a6e08257ca4d124392f80d208a6450","source":{"kind":"arxiv","id":"1104.5101","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.5101","created_at":"2026-05-18T04:15:59Z"},{"alias_kind":"arxiv_version","alias_value":"1104.5101v2","created_at":"2026-05-18T04:15:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.5101","created_at":"2026-05-18T04:15:59Z"},{"alias_kind":"pith_short_12","alias_value":"RVGXVJMELTMD","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_16","alias_value":"RVGXVJMELTMDM36A","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_8","alias_value":"RVGXVJME","created_at":"2026-05-18T12:26:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:RVGXVJMELTMDM36AJHGKXQEEEW","target":"record","payload":{"canonical_record":{"source":{"id":"1104.5101","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.QA","submitted_at":"2011-04-27T09:56:59Z","cross_cats_sorted":[],"title_canon_sha256":"4085810574c2890c707292bc9e1ea3dff200db7da4c00667f7319ab052a4eb22","abstract_canon_sha256":"4d0d82ac154a731e02727ae0f2269ccea300633e54a52c7cde287a7adb0bdc18"},"schema_version":"1.0"},"canonical_sha256":"8d4d7aa5845cd8366fc049ccabc08425b5a6e08257ca4d124392f80d208a6450","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:15:59.297992Z","signature_b64":"NlG5cNdf4LG31QtnJIWADO8Ue7KRmBeJheCQ8N41jj6xifqfx2XO3P4ry3YrSafhbV+3au+kKCSb02xkNGO4Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8d4d7aa5845cd8366fc049ccabc08425b5a6e08257ca4d124392f80d208a6450","last_reissued_at":"2026-05-18T04:15:59.297329Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:15:59.297329Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1104.5101","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:15:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RbIkAnuW2WqP2R6iEn9Kl2NTwXfMkpa8h0wL6aQKA2xWmrQhETQdV8HkFBGlek38e1H+UHhE8Y0fFn083GLWBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T13:21:26.112672Z"},"content_sha256":"86a6dd713911d4e9a53adc1a7c120fa254f338be706078932fbb895b54cd216f","schema_version":"1.0","event_id":"sha256:86a6dd713911d4e9a53adc1a7c120fa254f338be706078932fbb895b54cd216f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:RVGXVJMELTMDM36AJHGKXQEEEW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quantum Analogs of Tensor Product Representations of su(1,1)","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Wolter Groenevelt","submitted_at":"2011-04-27T09:56:59Z","abstract_excerpt":"We study representations of $U_q(su(1,1))$ that can be considered as quantum analogs of tensor products of irreducible *-representations of the Lie algebra $su(1,1)$. We determine the decomposition of these representations into irreducible *-representations of $U_q(su(1,1))$ by diagonalizing the action of the Casimir operator on suitable subspaces of the representation spaces. This leads to an interpretation of the big $q$-Jacobi polynomials and big $q$-Jacobi functions as quantum analogs of Clebsch-Gordan coefficients."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.5101","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:15:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iBU/XXE133zQMBHoy7yZ3bY1IpPcGX/Cr1lGjhJ/8Z51bCPhxodxlbkWMhcFAtfIhAIMLZ0fSSbVwLQoEDLhBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T13:21:26.113009Z"},"content_sha256":"cb456241a8aca95b252ff6e4fa820dbec22075023ba55993ba0b73f566d30baf","schema_version":"1.0","event_id":"sha256:cb456241a8aca95b252ff6e4fa820dbec22075023ba55993ba0b73f566d30baf"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RVGXVJMELTMDM36AJHGKXQEEEW/bundle.json","state_url":"https://pith.science/pith/RVGXVJMELTMDM36AJHGKXQEEEW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RVGXVJMELTMDM36AJHGKXQEEEW/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-26T13:21:26Z","links":{"resolver":"https://pith.science/pith/RVGXVJMELTMDM36AJHGKXQEEEW","bundle":"https://pith.science/pith/RVGXVJMELTMDM36AJHGKXQEEEW/bundle.json","state":"https://pith.science/pith/RVGXVJMELTMDM36AJHGKXQEEEW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RVGXVJMELTMDM36AJHGKXQEEEW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:RVGXVJMELTMDM36AJHGKXQEEEW","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":"4d0d82ac154a731e02727ae0f2269ccea300633e54a52c7cde287a7adb0bdc18","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.QA","submitted_at":"2011-04-27T09:56:59Z","title_canon_sha256":"4085810574c2890c707292bc9e1ea3dff200db7da4c00667f7319ab052a4eb22"},"schema_version":"1.0","source":{"id":"1104.5101","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.5101","created_at":"2026-05-18T04:15:59Z"},{"alias_kind":"arxiv_version","alias_value":"1104.5101v2","created_at":"2026-05-18T04:15:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.5101","created_at":"2026-05-18T04:15:59Z"},{"alias_kind":"pith_short_12","alias_value":"RVGXVJMELTMD","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_16","alias_value":"RVGXVJMELTMDM36A","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_8","alias_value":"RVGXVJME","created_at":"2026-05-18T12:26:41Z"}],"graph_snapshots":[{"event_id":"sha256:cb456241a8aca95b252ff6e4fa820dbec22075023ba55993ba0b73f566d30baf","target":"graph","created_at":"2026-05-18T04:15:59Z","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 study representations of $U_q(su(1,1))$ that can be considered as quantum analogs of tensor products of irreducible *-representations of the Lie algebra $su(1,1)$. We determine the decomposition of these representations into irreducible *-representations of $U_q(su(1,1))$ by diagonalizing the action of the Casimir operator on suitable subspaces of the representation spaces. This leads to an interpretation of the big $q$-Jacobi polynomials and big $q$-Jacobi functions as quantum analogs of Clebsch-Gordan coefficients.","authors_text":"Wolter Groenevelt","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.QA","submitted_at":"2011-04-27T09:56:59Z","title":"Quantum Analogs of Tensor Product Representations of su(1,1)"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.5101","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":"sha256:86a6dd713911d4e9a53adc1a7c120fa254f338be706078932fbb895b54cd216f","target":"record","created_at":"2026-05-18T04:15:59Z","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":"4d0d82ac154a731e02727ae0f2269ccea300633e54a52c7cde287a7adb0bdc18","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.QA","submitted_at":"2011-04-27T09:56:59Z","title_canon_sha256":"4085810574c2890c707292bc9e1ea3dff200db7da4c00667f7319ab052a4eb22"},"schema_version":"1.0","source":{"id":"1104.5101","kind":"arxiv","version":2}},"canonical_sha256":"8d4d7aa5845cd8366fc049ccabc08425b5a6e08257ca4d124392f80d208a6450","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8d4d7aa5845cd8366fc049ccabc08425b5a6e08257ca4d124392f80d208a6450","first_computed_at":"2026-05-18T04:15:59.297329Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:15:59.297329Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NlG5cNdf4LG31QtnJIWADO8Ue7KRmBeJheCQ8N41jj6xifqfx2XO3P4ry3YrSafhbV+3au+kKCSb02xkNGO4Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:15:59.297992Z","signed_message":"canonical_sha256_bytes"},"source_id":"1104.5101","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:86a6dd713911d4e9a53adc1a7c120fa254f338be706078932fbb895b54cd216f","sha256:cb456241a8aca95b252ff6e4fa820dbec22075023ba55993ba0b73f566d30baf"],"state_sha256":"56ca0c6894e6781c7bd0fe513a46e050af89240ac115dd8c9b529f9533073d50"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3B0gsTJK/KJZHP1g4sumRhJU8uG15tYcJgI+Bb0WEwTcSIRyXJl9bPWT7tn2KUCWCVEVzG27fAX3QoofT+orBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T13:21:26.115186Z","bundle_sha256":"a840d4d2045f479a3b794c54139f16332bc73ae7474dbfc3db37eea5ae15b57f"}}