{"paper":{"title":"The universal DAHA of type $(C_1^\\vee,C_1)$ and Leonard pairs of $q$-Racah type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Kazumasa Nomura, Paul Terwilliger","submitted_at":"2017-01-21T21:34:33Z","abstract_excerpt":"A Leonard pair is a pair of diagonalizable linear transformations of a finite-dimensional vector space, each of which acts in an irreducible tridiagonal fashion on an eigenbasis for the other one. Let $\\mathbb F$ denote an algebraically closed field, and fix a nonzero $q \\in \\mathbb F$ that is not a root of unity. The universal double affine Hecke algebra (DAHA) $\\hat{H}_q$ of type $(C_1^\\vee,C_1)$ is the associative $\\mathbb F$-algebra defined by generators $\\lbrace t_i^{\\pm 1}\\rbrace_{i=0}^3$ and relations (i) $t_it_i^{-1}=t_i^{-1}t_i=1$; (ii) $t_i+t_i^{-1}$ is central; (iii) $t_0t_1t_2t_3 ="},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.06089","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"}