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faculty: "FNWI" and publication year: "2007"
| Author||T.H. Koornwinder|
|Title||The Relationship between Zhedanov's Algebra AW(3) and the Double Affine Hecke Algebra in the Rank One Case|
|Journal||Symmetry, Integrability and Geometry : Methods and Applications (SIGMA)|
|Faculty||Faculty of Science|
|Institute/dept.||FNWI: Korteweg-de Vries Institute for Mathematics (KdVI)|
|Abstract||Vadim Kuznetsov Memorial Issue on Integrable Systems and Related Topics|
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) such that the Casimir operator is equal to a special constant. Some explicit aspects of the double affine Hecke algebra (DAHA) related to symmetric and non-symmetric Askey-Wilson polynomials are presented and proved without requiring knowledge of general DAHA theory. Finally a central extension of this quotient of AW(3) is introduced which can be embedded in the DAHA by means of the faithful basic representations of both algebras.
Key words: Zhedanov's algebra AW(3); double affine Hecke algebra in rank one; Askey-Wilson polynomials; non-symmetric Askey-Wilson polynomials.
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