{"paper":{"title":"Non-Symmetric Basic Hypergeometric Polynomials and Representation Theory for Confluent Cherednik Algebras","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":["math-ph","math.MP","nlin.SI"],"primary_cat":"math.QA","authors_text":"Marta Mazzocco","submitted_at":"2014-09-15T15:10:16Z","abstract_excerpt":"In this paper we introduce a basic representation for the confluent Cherednik algebras $\\mathcal H_{\\rm V}$, $\\mathcal H_{\\rm III}$, $\\mathcal H_{\\rm III}^{D_7}$ and $\\mathcal H_{\\rm III}^{D_8}$ defined in arXiv:1307.6140. To prove faithfulness of this basic representation, we introduce the non-symmetric versions of the continuous dual $q$-Hahn, Al-Salam-Chihara, continuous big $q$-Hermite and continuous $q$-Hermite polynomials."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.4287","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"}