{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2021:F7AHWKEI24RH6CEPEFJSAC5BVM","short_pith_number":"pith:F7AHWKEI","schema_version":"1.0","canonical_sha256":"2fc07b2888d7227f088f2153200ba1ab23af095f15d619a103b446d81d179e55","source":{"kind":"arxiv","id":"2106.06888","version":2},"attestation_state":"computed","paper":{"title":"Serre-Lusztig relations for $\\imath$quantum groups III","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.QA","authors_text":"Ming Lu, Weiqiang Wang, Xinhong Chen","submitted_at":"2021-06-13T00:49:45Z","abstract_excerpt":"let $\\widetilde{\\bf U}^\\imath$ be a quasi-split universal $\\imath$quantum group associated to a quantum symmetric pair $(\\widetilde{\\bf U}, \\widetilde{\\bf U}^\\imath)$ of Kac-Moody type with a diagram involution $\\tau$. We establish the Serre-Lusztig relations for $\\widetilde{\\bf U}^\\imath$ associated to a simple root $i$ such that $i \\neq \\tau i$, complementary to the Serre-Lusztig relations associated to $i=\\tau i$ which we obtained earlier. A conjecture on braid group symmetries on $\\widetilde{\\bf U}^\\imath$ associated to $i$ disjoint from $\\tau i$ is formulated."},"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":"2106.06888","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.QA","submitted_at":"2021-06-13T00:49:45Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"a44945debf4d285afc6f5ff94976cc6fb3199c93cce89696d3dc5c53df7575cf","abstract_canon_sha256":"230d4e3afe3fdf7d00b2bc8cc72e4ece9fc0b5613b992a1e4ddbb5423269dc88"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:17:59.380490Z","signature_b64":"E0vYAYIrbSwFq1n5W6ZE5Jud1Vm8ZZIwDvJF/MtYgdhSQCq+av6VPDe+yEBpJPNqgfwDzcvBskqOb0/gW7nDAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2fc07b2888d7227f088f2153200ba1ab23af095f15d619a103b446d81d179e55","last_reissued_at":"2026-07-05T05:17:59.380069Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:17:59.380069Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Serre-Lusztig relations for $\\imath$quantum groups III","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.QA","authors_text":"Ming Lu, Weiqiang Wang, Xinhong Chen","submitted_at":"2021-06-13T00:49:45Z","abstract_excerpt":"let $\\widetilde{\\bf U}^\\imath$ be a quasi-split universal $\\imath$quantum group associated to a quantum symmetric pair $(\\widetilde{\\bf U}, \\widetilde{\\bf U}^\\imath)$ of Kac-Moody type with a diagram involution $\\tau$. We establish the Serre-Lusztig relations for $\\widetilde{\\bf U}^\\imath$ associated to a simple root $i$ such that $i \\neq \\tau i$, complementary to the Serre-Lusztig relations associated to $i=\\tau i$ which we obtained earlier. A conjecture on braid group symmetries on $\\widetilde{\\bf U}^\\imath$ associated to $i$ disjoint from $\\tau i$ is formulated."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2106.06888","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2106.06888/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2106.06888","created_at":"2026-07-05T05:17:59.380124+00:00"},{"alias_kind":"arxiv_version","alias_value":"2106.06888v2","created_at":"2026-07-05T05:17:59.380124+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2106.06888","created_at":"2026-07-05T05:17:59.380124+00:00"},{"alias_kind":"pith_short_12","alias_value":"F7AHWKEI24RH","created_at":"2026-07-05T05:17:59.380124+00:00"},{"alias_kind":"pith_short_16","alias_value":"F7AHWKEI24RH6CEP","created_at":"2026-07-05T05:17:59.380124+00:00"},{"alias_kind":"pith_short_8","alias_value":"F7AHWKEI","created_at":"2026-07-05T05:17:59.380124+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/F7AHWKEI24RH6CEPEFJSAC5BVM","json":"https://pith.science/pith/F7AHWKEI24RH6CEPEFJSAC5BVM.json","graph_json":"https://pith.science/api/pith-number/F7AHWKEI24RH6CEPEFJSAC5BVM/graph.json","events_json":"https://pith.science/api/pith-number/F7AHWKEI24RH6CEPEFJSAC5BVM/events.json","paper":"https://pith.science/paper/F7AHWKEI"},"agent_actions":{"view_html":"https://pith.science/pith/F7AHWKEI24RH6CEPEFJSAC5BVM","download_json":"https://pith.science/pith/F7AHWKEI24RH6CEPEFJSAC5BVM.json","view_paper":"https://pith.science/paper/F7AHWKEI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2106.06888&json=true","fetch_graph":"https://pith.science/api/pith-number/F7AHWKEI24RH6CEPEFJSAC5BVM/graph.json","fetch_events":"https://pith.science/api/pith-number/F7AHWKEI24RH6CEPEFJSAC5BVM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/F7AHWKEI24RH6CEPEFJSAC5BVM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/F7AHWKEI24RH6CEPEFJSAC5BVM/action/storage_attestation","attest_author":"https://pith.science/pith/F7AHWKEI24RH6CEPEFJSAC5BVM/action/author_attestation","sign_citation":"https://pith.science/pith/F7AHWKEI24RH6CEPEFJSAC5BVM/action/citation_signature","submit_replication":"https://pith.science/pith/F7AHWKEI24RH6CEPEFJSAC5BVM/action/replication_record"}},"created_at":"2026-07-05T05:17:59.380124+00:00","updated_at":"2026-07-05T05:17:59.380124+00:00"}