# Double Affine Hecke Algebra of Rank 1 and Orthogonal Polynomials on the Unit Circle

@article{Tsujimoto2019DoubleAH, title={Double Affine Hecke Algebra of Rank 1 and Orthogonal Polynomials on the Unit Circle}, author={Satoshi Tsujimoto and Luc Vinet and Alexei S. Zhedanov}, journal={Constructive Approximation}, year={2019} }

An inifinite-dimensional representation of the double affine Hecke algebra of rank 1 and type $(C_1^{\vee},C_1)$ in which all generators are tridiagonal is presented. This representation naturally leads to two systems of polynomials that are orthogonal on the unit circle. These polynomials can be considered as circle analogs of the Askey-Wilson polynomials. The corresponding polynomials orthogonal on an interval are constructed and discussed.

#### 3 Citations

Dualities in the q
-Askey Scheme and Degenerate DAHA

- Mathematics, PhysicsStudies in Applied Mathematics
- 2018

The Askey–Wilson polynomials are a four-parameter family of orthogonal symmetric Laurent polynomials Rn[z] that are eigenfunctions of a second-order q-difference operator L, and of a second-order…

Finite-dimensional modules of the universal Askey–Wilson algebra and DAHA of type $$(C_1^\vee ,C_1)$$

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- 2020

Assume that $\mathbb F$ is an algebraically closed field and let $q$ denote a nonzero scalar in $\mathbb F$ that is not a root of unity. The universal Askey--Wilson algebra $\triangle_q$ is a unital…

The Askey–Wilson algebra and its avatars

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- 2020

The original Askey–Wilson algebra introduced by Zhedanov encodes the bispectrality properties of the eponym polynomials. The name Askey–Wilson algebra is currently used to refer to a variety of…

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