{"paper":{"title":"The algebra $U_q({\\mathfrak{sl}_2})$ in disguise","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.RT","authors_text":"Paul Terwilliger, Sarah Bockting-Conrad","submitted_at":"2013-07-29T13:37:00Z","abstract_excerpt":"We discuss a connection between the algebra $U_q({\\mathfrak{sl}_2})$ and the tridiagonal pairs of $q$-Racah type. To describe the connection, let $x,y^{\\pm 1},z$ denote the equitable generators for $U_q({\\mathfrak{sl}_2})$. Let $U^\\vee_q$ denote the subalgebra of $U_q({\\mathfrak{sl}_2})$ generated by $x,y^{-1},z$. Using a tridiagonal pair of $q$-Racah type we construct two finite-dimensional $U^\\vee_q$-modules. The constructions yield two nonstandard presentations of $U^\\vee_q$ by generators and relations. These presentations are investigated in detail."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.7572","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"}