{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:LH4XTLI7DUS2HE7SWP7KEZK23Q","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":"7008be97a60947db9206a345751104cf92cad0bd93a4a13c78ab0b8302f57133","cross_cats_sorted":["math.QA"],"license":"","primary_cat":"math.OA","submitted_at":"2006-09-25T02:39:40Z","title_canon_sha256":"e7df95f11611309af27203ce3d4b757c32023047c4430f7f19db7fd453fee336"},"schema_version":"1.0","source":{"id":"math/0609676","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0609676","created_at":"2026-07-04T14:56:36Z"},{"alias_kind":"arxiv_version","alias_value":"math/0609676v1","created_at":"2026-07-04T14:56:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0609676","created_at":"2026-07-04T14:56:36Z"},{"alias_kind":"pith_short_12","alias_value":"LH4XTLI7DUS2","created_at":"2026-07-04T14:56:36Z"},{"alias_kind":"pith_short_16","alias_value":"LH4XTLI7DUS2HE7S","created_at":"2026-07-04T14:56:36Z"},{"alias_kind":"pith_short_8","alias_value":"LH4XTLI7","created_at":"2026-07-04T14:56:36Z"}],"graph_snapshots":[{"event_id":"sha256:55f70bbc8ae0b9b9681b1d6305247244ff4be1038d84a4fe7c1b1b54534ab3e5","target":"graph","created_at":"2026-07-04T14:56:36Z","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/0609676/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let v be the right regular representation of a compact quantum group G. Then (S.L.Woronowicz, \"Compact quantum groups\") v contains all irreducible representations of G and each irreducible representation enters v with the multiplicity equal to its dimension. The result is certainly known for classical compact groups. We give a short survey on the subject and provide a different proof of Woronowicz's result above. The proof is an adaptation of the corresponding result for classical compact groups and provides a concrete decomposition of the right regular representation in irreducible components","authors_text":"Raluca Dumitru","cross_cats":["math.QA"],"headline":"","license":"","primary_cat":"math.OA","submitted_at":"2006-09-25T02:39:40Z","title":"Unitary representations of compact quantum groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0609676","kind":"arxiv","version":1},"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:ec564046efd20189078540d17646b57f947f5258a52760cf016a4cd595103172","target":"record","created_at":"2026-07-04T14:56:36Z","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":"7008be97a60947db9206a345751104cf92cad0bd93a4a13c78ab0b8302f57133","cross_cats_sorted":["math.QA"],"license":"","primary_cat":"math.OA","submitted_at":"2006-09-25T02:39:40Z","title_canon_sha256":"e7df95f11611309af27203ce3d4b757c32023047c4430f7f19db7fd453fee336"},"schema_version":"1.0","source":{"id":"math/0609676","kind":"arxiv","version":1}},"canonical_sha256":"59f979ad1f1d25a393f2b3fea2655adc1d5e7239373f0aec9843a2d1b00b105a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"59f979ad1f1d25a393f2b3fea2655adc1d5e7239373f0aec9843a2d1b00b105a","first_computed_at":"2026-07-04T14:56:36.121403Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:56:36.121403Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9w26niyxhkmLqGP3yl0LFkYuA9ilUugbEWJkc00xJDJW5BtoRr4DVOoAYt1ZCK4mzXHbCK+YZHdIRCCrb0h2Cg==","signature_status":"signed_v1","signed_at":"2026-07-04T14:56:36.121839Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0609676","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ec564046efd20189078540d17646b57f947f5258a52760cf016a4cd595103172","sha256:55f70bbc8ae0b9b9681b1d6305247244ff4be1038d84a4fe7c1b1b54534ab3e5"],"state_sha256":"b19f34df86b1f6c80d029a7c78faae67f39fab4053a8865fe7dd3c9abb60ad96"}