{"paper":{"title":"Distance-regular graphs of $q$-Racah type and the universal Askey-Wilson algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.CO","authors_text":"Arjana \\v{Z}itnik, Paul Terwilliger","submitted_at":"2013-07-30T13:26:47Z","abstract_excerpt":"Let $\\C$ denote the field of complex numbers, and fix a nonzero $q \\in \\C$ such that $q^4 \\ne 1$. Define a $\\C$-algebra $\\Delta_q$ 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 algebra $\\Delta_q$ is called the universal Askey-Wilson algebra. Let $\\Gamma$ denote a distance-regular graph that has $q$-Racah type. Fix a vertex $x$ of $\\Gamma$ and let $T=T(x)$ denote the corresponding subconstitu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.7968","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"}