{"paper":{"title":"Dualities in the $q$-Askey scheme and degenerate DAHA","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA","nlin.SI"],"primary_cat":"math.CA","authors_text":"Marta Mazzocco, Tom H. Koornwinder","submitted_at":"2018-03-07T17:14:21Z","abstract_excerpt":"The Askey-Wilson polynomials are a four-parameter family of orthogonal symmetric Laurent polynomials $R_n[z]$ which are eigenfunctions of a second-order $q$-difference operator $L$, and of a second-order difference operator in the variable $n$ with eigenvalue $z +z^{-1}=2x$. Then $L$ and multiplication by $z+z^{-1}$ generate the Askey-Wilson (Zhedanov) algebra. A nice property of the Askey-Wilson polynomials is that the variables $z$ and $n$ occur in the explicit expression in a similar and to some extent exchangeable way. This property is called duality. It returns in the non-symmetric case a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.02775","kind":"arxiv","version":3},"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"}