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

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2014
• Main Author: Mazzocco, M.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2014
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/146401
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Non-symmetric basic hypergeometric polynomials and representation theory for confluent cherednik algebras / M. Mazzocco // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — англ.

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 b...