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Non-Symmetric Basic Hypergeometric Polynomials and Representation Theory for Confluent Cherednik Algebras
Symmetry, integrability and geometry: methods and applications, Tome 10 (2014) Cet article a éte moissonné depuis la source Math-Net.Ru

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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.
Keywords: DAHA; Cherednik algebra; $q$-Askey scheme; Askey–Wilson polynomials. 
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     author = {Marta Mazzocco},
     title = {Non-Symmetric {Basic} {Hypergeometric} {Polynomials} and {Representation} {Theory} for {Confluent} {Cherednik} {Algebras}},
     journal = {Symmetry, integrability and geometry: methods and applications},
     year = {2014},
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     url = {http://geodesic.mathdoc.fr/item/SIGMA_2014_10_a115/}
}
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Marta Mazzocco. Non-Symmetric Basic Hypergeometric Polynomials and Representation Theory for Confluent Cherednik Algebras. Symmetry, integrability and geometry: methods and applications, Tome 10 (2014). http://geodesic.mathdoc.fr/item/SIGMA_2014_10_a115/

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