{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2002:LDBKBH7NDH32CRBINVYJ7P6NRM","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":"f081e3ae06967e28a72ad3c2309fe84f429fe0ceb0cea0b2f5347c49dec177e0","cross_cats_sorted":["hep-th"],"license":"","primary_cat":"math.QA","submitted_at":"2002-08-23T19:49:53Z","title_canon_sha256":"afc97d23c274fd166103e2904152d104b8145328da1646103d7bdbf47957e18a"},"schema_version":"1.0","source":{"id":"math/0208191","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0208191","created_at":"2026-07-04T16:35:04Z"},{"alias_kind":"arxiv_version","alias_value":"math/0208191v2","created_at":"2026-07-04T16:35:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0208191","created_at":"2026-07-04T16:35:04Z"},{"alias_kind":"pith_short_12","alias_value":"LDBKBH7NDH32","created_at":"2026-07-04T16:35:04Z"},{"alias_kind":"pith_short_16","alias_value":"LDBKBH7NDH32CRBI","created_at":"2026-07-04T16:35:04Z"},{"alias_kind":"pith_short_8","alias_value":"LDBKBH7N","created_at":"2026-07-04T16:35:04Z"}],"graph_snapshots":[{"event_id":"sha256:7bf8ebead76d90b459313dad1997b34a4c8de71ad2d97d720266eacd6a1b8ee3","target":"graph","created_at":"2026-07-04T16:35:04Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/math/0208191/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A certain class of unitary representations of U_q(sl(2,R)) has the property of being simultanenously a representation of U_{tilde{q}}(sl(2,R)) for a particular choice of tilde{q}(q). Faddeev has proposed to unify the quantum groups U_q(sl(2,R)) and U_{tilde{q}}(sl(2,R)) into some enlarged object for which he has coined the name ``modular double''. We study the R-operator, the co-product and the Haar-measure for the modular double of U_q(sl(2,R)) and establish their main properties. In particular it is shown that the Clebsch-Gordan maps constructed in [PT2] diagonalize this R-operator.","authors_text":"A. Bytsko, J. Teschner","cross_cats":["hep-th"],"headline":"","license":"","primary_cat":"math.QA","submitted_at":"2002-08-23T19:49:53Z","title":"R-operator, co-product and Haar-measure for the modular double of U_q(sl(2,R))"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0208191","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":"sha256:89bd9995dcc719dd5f678770043a3a81fbee0e576531c96f82e70938af60b9eb","target":"record","created_at":"2026-07-04T16:35:04Z","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":"f081e3ae06967e28a72ad3c2309fe84f429fe0ceb0cea0b2f5347c49dec177e0","cross_cats_sorted":["hep-th"],"license":"","primary_cat":"math.QA","submitted_at":"2002-08-23T19:49:53Z","title_canon_sha256":"afc97d23c274fd166103e2904152d104b8145328da1646103d7bdbf47957e18a"},"schema_version":"1.0","source":{"id":"math/0208191","kind":"arxiv","version":2}},"canonical_sha256":"58c2a09fed19f7a144286d709fbfcd8b0b68d35d19175bc8566b9e74e6ef6cc8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"58c2a09fed19f7a144286d709fbfcd8b0b68d35d19175bc8566b9e74e6ef6cc8","first_computed_at":"2026-07-04T16:35:04.257984Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T16:35:04.257984Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ItaY05DnZqaqVqUsN4jod4wqi1XvGiZs20k/xSxWnHvMllFYPVfyvd75AbUdaUnWp15hw6HOpLcJfckHtwvgBg==","signature_status":"signed_v1","signed_at":"2026-07-04T16:35:04.258429Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0208191","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:89bd9995dcc719dd5f678770043a3a81fbee0e576531c96f82e70938af60b9eb","sha256:7bf8ebead76d90b459313dad1997b34a4c8de71ad2d97d720266eacd6a1b8ee3"],"state_sha256":"f4f1e8380b060abd51f91f4a475ab04f6c0459f013977ed32c86082a6933517f"}