Non-Symmetric Basic Hypergeometric Polynomials and Representation Theory for Confluent Cherednik Algebras

Abstract

In this paper we introduce a basic representation for the confluent Cherednik algebras HV, HIII, H7 III and H D8 III defined in arXiv:1307.6140. To prove faithfulness of this basic representation, we introduce the non-symmetric versions of the continuous dual qHahn, Al-Salam–Chihara, continuous big q-Hermite and continuous q-Hermite polynomials. 

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