The Relationship between Zhedanov's Algebra AW(3) and the Double Affine Hecke Algebra in the Rank One Case

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2007
• Main Author: Koornwinder, T.H.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2007
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/147378
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: The Relationship between Zhedanov's Algebra AW(3) and the Double Affine Hecke Algebra in the Rank One Case / T.H. Koornwinder // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 16 назв. — англ.

Zhedanov's algebra AW(3) is considered with explicit structure constants such that, in the basic representation, the first generator becomes the second order q-difference operator for the Askey-Wilson polynomials. It is proved that this representation is faithful for a certain quotient of AW(3)...