Non-symmetric basic hypergeometric polynomials and representation theory for confluent Cherednik algebras

2015-04-13T12:41:16Z (GMT) by Marta Mazzocco
In this paper we introduce a basic representation for the confluent Cherednik algebras HV, HIII, HD7 III and HD8 III 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.