{"paper":{"title":"On a Certain Subalgebra of $U_q(\\widehat{\\mathfrak{sl}}_2)$ Related to the Degenerate $q$-Onsager Algebra","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Tatsuro Ito, Tomoya Hattai","submitted_at":"2012-05-14T06:24:31Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.2946","kind":"arxiv","version":3},"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"}