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Zhedanov's Algebra $AW(3)$ and the Double Affine Hecke Algebra in the Rank One Case. II. The Spherical Subalgebra
Symmetry, integrability and geometry: methods and applications, Tome 4 (2008) Cet article a éte moissonné depuis la source Math-Net.Ru

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This paper builds on the previous paper by the author, where a relationship between Zhedanov's algebra $AW(3)$ and the double affine Hecke algebra (DAHA) corresponding to the Askey–Wilson polynomials was established. It is shown here that the spherical subalgebra of this DAHA is isomorphic to $AW(3)$ with an additional relation that the Casimir operator equals an explicit constant. A similar result with $q$-shifted parameters holds for the antispherical subalgebra. Some theorems on centralizers and centers for the algebras under consideration will finally be proved as corollaries of the characterization of the spherical and antispherical subalgebra.
Keywords: Zhedanov's algebra $AW(3)$; double affine Hecke algebra in rank one; Askey–Wilson polynomials; spherical subalgebra. 
@article{SIGMA_2008_4_a51,
     author = {Tom H. Koornwinder},
     title = {Zhedanov's {Algebra} $AW(3)$ and the {Double} {Affine} {Hecke} {Algebra} in the {Rank} {One} {Case.} {II.~The} {Spherical} {Subalgebra}},
     journal = {Symmetry, integrability and geometry: methods and applications},
     year = {2008},
     volume = {4},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2008_4_a51/}
}
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Tom H. Koornwinder. Zhedanov's Algebra $AW(3)$ and the Double Affine Hecke Algebra in the Rank One Case. II. The Spherical Subalgebra. Symmetry, integrability and geometry: methods and applications, Tome 4 (2008). http://geodesic.mathdoc.fr/item/SIGMA_2008_4_a51/

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