{"paper":{"title":"The quantum loop algebra of $sl_2$ and $q$-Racah type bivariate functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.RT"],"primary_cat":"math.QA","authors_text":"Nicolas Crampe, Pascal Baseilhac","submitted_at":"2026-07-22T11:38:00Z","abstract_excerpt":"A unified algebraic framework for two different six-parameter families of bivariate $q$-Racah type functions is given using the representation theory of the quantum loop algebra $\\mathcal{L} U_q sl_2$ of $sl_2$. The starting point of the analysis is two left and right coideal subalgebras of $\\mathcal{L} U_q sl_2$ and six commutative subalgebras, built from eight elements in $\\mathcal{L} U_q sl_2 \\otimes \\mathcal{L} U_q sl_2$. The eight elements depend on two scalars $a,b \\in {\\mathbb C}^*$, and are diagonalized on a finite-dimensional vector space. The bivariate $q$-Racah type functions are in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.20043","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.20043/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"}