{"paper":{"title":"The Universal Askey-Wilson Algebra and DAHA of Type $(C_1^{\\vee},C_1)$","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Paul Terwilliger","submitted_at":"2012-02-21T15:29:36Z","abstract_excerpt":"Let $\\mathbb F$ denote a field, and fix a nonzero $q\\in\\mathbb F$ such that $q^4\\not=1$. The universal Askey-Wilson algebra $\\Delta_q$ is the associative $\\mathbb F$-algebra defined by generators and relations in the following way. The generators are $A$, $B$, $C$. The relations assert that each of $A+\\frac{qBC-q^{-1}CB}{q^2-q^{-2}}$, $B+\\frac{qCA-q^{-1}AC}{q^2-q^{-2}}$, $C+\\frac{qAB-q^{-1}BA}{q^2-q^{-2}}$ is central in $\\Delta_q$. The universal DAHA $\\hat H_q$ of type $(C_1^\\vee,C_1)$ is the associative $\\mathbb F$-algebra defined by generators $\\lbrace t^{\\pm1}_i\\rbrace_{i=0}^3$ and relation"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.4673","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"}