Non-symmetric basic hypergeometric polynomials and representation theory for confluent cherednik algebras - Mazzocco, M. (Symmetry, Integrability and Geometry: Methods and Applications, 2014)
In this paper we introduce a basic representation for the confluent Cherednik
algebras HV, HIII, HD7III and HD8III 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.