{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2004:IWCB3PVGDV3EV6YZKY3J472VLR","short_pith_number":"pith:IWCB3PVG","canonical_record":{"source":{"id":"math/0406343","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.QA","submitted_at":"2004-06-17T14:16:47Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"47448d3c45c01c55abe73866c5e90c2db04ea88a2212733587a5b4b70a273bfe","abstract_canon_sha256":"b8ddf3e11735d4f6dc66f4f85fed30739f2343c5b931bf7c2feb70ce106a8837"},"schema_version":"1.0"},"canonical_sha256":"45841dbea61d764afb1956369e7f555c43762a359eddadd05e08b9e9c7f0430c","source":{"kind":"arxiv","id":"math/0406343","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0406343","created_at":"2026-05-18T01:38:27Z"},{"alias_kind":"arxiv_version","alias_value":"math/0406343v1","created_at":"2026-05-18T01:38:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0406343","created_at":"2026-05-18T01:38:27Z"},{"alias_kind":"pith_short_12","alias_value":"IWCB3PVGDV3E","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"IWCB3PVGDV3EV6YZ","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"IWCB3PVG","created_at":"2026-05-18T12:25:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2004:IWCB3PVGDV3EV6YZKY3J472VLR","target":"record","payload":{"canonical_record":{"source":{"id":"math/0406343","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.QA","submitted_at":"2004-06-17T14:16:47Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"47448d3c45c01c55abe73866c5e90c2db04ea88a2212733587a5b4b70a273bfe","abstract_canon_sha256":"b8ddf3e11735d4f6dc66f4f85fed30739f2343c5b931bf7c2feb70ce106a8837"},"schema_version":"1.0"},"canonical_sha256":"45841dbea61d764afb1956369e7f555c43762a359eddadd05e08b9e9c7f0430c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:38:27.288553Z","signature_b64":"1TlavJ3o1erXwVlSud3Wy1kA7kUl5QYzRhR+ty74AkdSw9t2VMJNNs9aLddEVEcVM+YhPwZkjCNRtpG9VEDXCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"45841dbea61d764afb1956369e7f555c43762a359eddadd05e08b9e9c7f0430c","last_reissued_at":"2026-05-18T01:38:27.287904Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:38:27.287904Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0406343","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:38:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"N4JxwGJFUqSCAfKOLJl30DxBFztTzrowSn2BV780nG9DE03+f/dpl89A5QqxA1Ltc0wQ+KnQzG92umf3zqEjBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T17:20:48.507181Z"},"content_sha256":"96aad8836a2b92fbfd55371af7097bbc40488a6470e38476fed7bc961688ec9a","schema_version":"1.0","event_id":"sha256:96aad8836a2b92fbfd55371af7097bbc40488a6470e38476fed7bc961688ec9a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2004:IWCB3PVGDV3EV6YZKY3J472VLR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Degenerate principal series of quantum Harish-Chandra modules","license":"","headline":"","cross_cats":["math.RT"],"primary_cat":"math.QA","authors_text":"Olga Bershtein","submitted_at":"2004-06-17T14:16:47Z","abstract_excerpt":"In this paper we study a quantum analogue of a degenerate principal series of $U_q \\mathfrak{su}_{n,n}$-modules ($0<q<1$) related to the Shilov boundary of the quantum $n \\times n$-matrix unit ball. We give necessary and sufficient conditions for the modules to be simple and unitarizable and investigate their equivalence.\n  These results are q-analogues of known classical results on reducibility and unitarizability of SU(n,n)-modules obtained by Johnson, Sahi, Zhang, Howe and Tan."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0406343","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:38:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iru7MkC7Ih580qH18Qw46y9W1Xldbou4zgZb+/AsyKxFsEJJGjt8HBGlvw/CObuNIljnAt/Tmywfonuy/LmIBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T17:20:48.507812Z"},"content_sha256":"1a525b70eca2eba45514e88bb6038b1097c48fb8d071827758f5d8a2b0f321bc","schema_version":"1.0","event_id":"sha256:1a525b70eca2eba45514e88bb6038b1097c48fb8d071827758f5d8a2b0f321bc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IWCB3PVGDV3EV6YZKY3J472VLR/bundle.json","state_url":"https://pith.science/pith/IWCB3PVGDV3EV6YZKY3J472VLR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IWCB3PVGDV3EV6YZKY3J472VLR/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":"2026-06-07T17:20:48Z","links":{"resolver":"https://pith.science/pith/IWCB3PVGDV3EV6YZKY3J472VLR","bundle":"https://pith.science/pith/IWCB3PVGDV3EV6YZKY3J472VLR/bundle.json","state":"https://pith.science/pith/IWCB3PVGDV3EV6YZKY3J472VLR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IWCB3PVGDV3EV6YZKY3J472VLR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2004:IWCB3PVGDV3EV6YZKY3J472VLR","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":"b8ddf3e11735d4f6dc66f4f85fed30739f2343c5b931bf7c2feb70ce106a8837","cross_cats_sorted":["math.RT"],"license":"","primary_cat":"math.QA","submitted_at":"2004-06-17T14:16:47Z","title_canon_sha256":"47448d3c45c01c55abe73866c5e90c2db04ea88a2212733587a5b4b70a273bfe"},"schema_version":"1.0","source":{"id":"math/0406343","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0406343","created_at":"2026-05-18T01:38:27Z"},{"alias_kind":"arxiv_version","alias_value":"math/0406343v1","created_at":"2026-05-18T01:38:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0406343","created_at":"2026-05-18T01:38:27Z"},{"alias_kind":"pith_short_12","alias_value":"IWCB3PVGDV3E","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"IWCB3PVGDV3EV6YZ","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"IWCB3PVG","created_at":"2026-05-18T12:25:52Z"}],"graph_snapshots":[{"event_id":"sha256:1a525b70eca2eba45514e88bb6038b1097c48fb8d071827758f5d8a2b0f321bc","target":"graph","created_at":"2026-05-18T01:38:27Z","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":"In this paper we study a quantum analogue of a degenerate principal series of $U_q \\mathfrak{su}_{n,n}$-modules ($0<q<1$) related to the Shilov boundary of the quantum $n \\times n$-matrix unit ball. We give necessary and sufficient conditions for the modules to be simple and unitarizable and investigate their equivalence.\n  These results are q-analogues of known classical results on reducibility and unitarizability of SU(n,n)-modules obtained by Johnson, Sahi, Zhang, Howe and Tan.","authors_text":"Olga Bershtein","cross_cats":["math.RT"],"headline":"","license":"","primary_cat":"math.QA","submitted_at":"2004-06-17T14:16:47Z","title":"Degenerate principal series of quantum Harish-Chandra modules"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0406343","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":"sha256:96aad8836a2b92fbfd55371af7097bbc40488a6470e38476fed7bc961688ec9a","target":"record","created_at":"2026-05-18T01:38:27Z","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":"b8ddf3e11735d4f6dc66f4f85fed30739f2343c5b931bf7c2feb70ce106a8837","cross_cats_sorted":["math.RT"],"license":"","primary_cat":"math.QA","submitted_at":"2004-06-17T14:16:47Z","title_canon_sha256":"47448d3c45c01c55abe73866c5e90c2db04ea88a2212733587a5b4b70a273bfe"},"schema_version":"1.0","source":{"id":"math/0406343","kind":"arxiv","version":1}},"canonical_sha256":"45841dbea61d764afb1956369e7f555c43762a359eddadd05e08b9e9c7f0430c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"45841dbea61d764afb1956369e7f555c43762a359eddadd05e08b9e9c7f0430c","first_computed_at":"2026-05-18T01:38:27.287904Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:38:27.287904Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1TlavJ3o1erXwVlSud3Wy1kA7kUl5QYzRhR+ty74AkdSw9t2VMJNNs9aLddEVEcVM+YhPwZkjCNRtpG9VEDXCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:38:27.288553Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0406343","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:96aad8836a2b92fbfd55371af7097bbc40488a6470e38476fed7bc961688ec9a","sha256:1a525b70eca2eba45514e88bb6038b1097c48fb8d071827758f5d8a2b0f321bc"],"state_sha256":"2f73866faefbfe0fe7e900cb90b4ee9a374be8b430a4678dc28746033ad3eee3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xZa2aIBKOXTYy3jJFYg3szptmhE/8D77+3SVuAWsuP1KSn/TvxuiehQLNFFwx2ZD5XLDGdRErJ4/O5UNKBvMBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T17:20:48.511309Z","bundle_sha256":"882e1697aa170786e0adebd36891ed369b72c04c5b3f02fd1f9e16ac896a4822"}}