The Relationship between Zhedanov's Algebra AW(3) and the Double Affine Hecke Algebra in the Rank One Case
By Tom H. Koornwinder. 2006
76 citations recorded by the source corpus.
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 faith- ful 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 sym- metric 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.
Subfields: Applied Mathematics, Atomic and Molecular Physics, and Optics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/b3c8088a9ee494ebf6464bca6fa7385e136650e7
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In Applied Mathematics
In Atomic and Molecular Physics, and Optics
In Geometry and Topology
Citations in the corpus
- Zhedanov's Algebra AW(3) and the Double Affine Hecke Algebra in the Rank One Case. II. The Spherical Subalgebra ? (2007, methodology): “It turns out (see [7]) that a central extension ÃW (3, Q0) of AW (3, Q0) can be embedded as a subalgebra of H̃.”