{"paper":{"title":"An embedding of the universal Askey-Wilson algebra into $U_q(\\mathfrak{sl}_2)\\otimes U_q(\\mathfrak{sl}_2)\\otimes U_q(\\mathfrak{sl}_2)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.QA","authors_text":"Hau-wen Huang","submitted_at":"2016-10-29T01:15:52Z","abstract_excerpt":"The Askey--Wilson algebras were used to interpret the algebraic structure hidden in the Racah--Wigner coefficients of the quantum algebra $U_q(\\mathfrak{sl}_2)$. In this paper, we display an injection of a universal analog $\\triangle_q$ of Askey--Wilson algebras into $U_q(\\mathfrak{sl}_2)\\otimes U_q(\\mathfrak{sl}_2)\\otimes U_q(\\mathfrak{sl}_2)$ behind the application. Moreover we formulate the decomposition rules for $3$-fold tensor products of irreducible Verma $U_q(\\mathfrak{sl}_2)$-modules and of finite-dimensional irreducible $U_q(\\mathfrak{sl}_2)$-modules into the direct sums of finite-di"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.02130","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":""},"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"}