{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:XGGZ7JTXFJVMWHRH7RP2QMTWBD","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":"490a86e5b85e222935de42ec54d195704c160379c0a8c4af38a166b62768c1dd","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.QA","submitted_at":"2012-05-14T06:24:31Z","title_canon_sha256":"bd42168aef98b1d49b42d030c1fb3377eccacf18e02c77c907888e72eb6082cf"},"schema_version":"1.0","source":{"id":"1205.2946","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.2946","created_at":"2026-05-18T02:29:16Z"},{"alias_kind":"arxiv_version","alias_value":"1205.2946v3","created_at":"2026-05-18T02:29:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.2946","created_at":"2026-05-18T02:29:16Z"},{"alias_kind":"pith_short_12","alias_value":"XGGZ7JTXFJVM","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"XGGZ7JTXFJVMWHRH","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"XGGZ7JTX","created_at":"2026-05-18T12:27:27Z"}],"graph_snapshots":[{"event_id":"sha256:eb910f4b2d410539046093da818d98020cd89d6b253988e129b8057ecf101c9c","target":"graph","created_at":"2026-05-18T02:29:16Z","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 [Kyushu J. Math. 64 (2010), 81-144, arXiv:0904.2889], it is discussed that a certain subalgebra of the quantum affine algebra $U_q(\\widehat{\\mathfrak{sl}}_2)$ controls the second kind TD-algebra of type I (the degenerate $q$-Onsager algebra). The subalgebra, which we denote by $U'_q(\\widehat{\\mathfrak{sl}}_2)$, is generated by $e_0^+$, $e_1^\\pm$, $k_i^{\\pm1}$ $(i=0,1)$ with $e^-_0$ missing from the Chevalley generators $e_i^\\pm$, $k_i^{\\pm1}$ $(i=0,1)$ of $U_q(\\widehat{\\mathfrak{sl}}_2)$. In this paper, we determine the finite-dimensional irreducible representations of $U'_q(\\widehat{\\mathf","authors_text":"Tatsuro Ito, Tomoya Hattai","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.QA","submitted_at":"2012-05-14T06:24:31Z","title":"On a Certain Subalgebra of $U_q(\\widehat{\\mathfrak{sl}}_2)$ Related to the Degenerate $q$-Onsager Algebra"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.2946","kind":"arxiv","version":3},"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":"sha256:57f38bc19adeeddb92bdcef16b94e69dce449855ca8924ee5c6c11d8eee6736b","target":"record","created_at":"2026-05-18T02:29:16Z","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":"490a86e5b85e222935de42ec54d195704c160379c0a8c4af38a166b62768c1dd","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.QA","submitted_at":"2012-05-14T06:24:31Z","title_canon_sha256":"bd42168aef98b1d49b42d030c1fb3377eccacf18e02c77c907888e72eb6082cf"},"schema_version":"1.0","source":{"id":"1205.2946","kind":"arxiv","version":3}},"canonical_sha256":"b98d9fa6772a6acb1e27fc5fa8327608ff76c85424db4a74f4359aa90e4593df","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b98d9fa6772a6acb1e27fc5fa8327608ff76c85424db4a74f4359aa90e4593df","first_computed_at":"2026-05-18T02:29:16.161633Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:29:16.161633Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+DPzxMOzhPXDulcD2PoI7a1sYAuLHdjPzxya+RSwdPKxbXSQv2EOCuPg5hTqcA8+V7DRjUpYoXVgAmdN/lLWBA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:29:16.161993Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.2946","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:57f38bc19adeeddb92bdcef16b94e69dce449855ca8924ee5c6c11d8eee6736b","sha256:eb910f4b2d410539046093da818d98020cd89d6b253988e129b8057ecf101c9c"],"state_sha256":"0cf68699574a39f1fc0f61e5b082bf63c9a41d92a4bb6d5af5fd05cf1750a176"}