Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 10 (2014), 116, 10 pages      arXiv:1409.4287

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

Marta Mazzocco
Department of Mathematical Sciences, Loughborough University, Loughborough LE11 3TU, UK

Received October 31, 2014, in final form December 19, 2014; Published online December 30, 2014

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.

Key words: DAHA; Cherednik algebra; $q$-Askey scheme; Askey-Wilson polynomials.

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