{"paper":{"title":"Double Affine Hecke Algebras of Rank 1 and the $Z_3$-Symmetric Askey-Wilson Relations","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.RA","authors_text":"Paul Terwilliger, Tatsuro Ito","submitted_at":"2010-01-15T20:42:33Z","abstract_excerpt":"We consider the double affine Hecke algebra $H=H(k_0,k_1,k^\\vee_0,k^\\vee_1;q)$ associated with the root system $(C^\\vee_1,C_1)$. We display three elements $x$, $y$, $z$ in $H$ that satisfy essentially the $Z_3$-symmetric Askey-Wilson relations. We obtain the relations as follows. We work with an algebra $\\hat H$ that is more general than $H$, called the universal double affine Hecke algebra of type $(C_1^\\vee,C_1)$. An advantage of $\\hat H$ over $H$ is that it is parameter free and has a larger automorphism group. We give a surjective algebra homomorphism ${\\hat H} \\to H$. We define some eleme"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1001.2764","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"}