Double affine Hecke algebra of rank 1 and orthogonal polynomials on the unit circle
Satoshi Tsujimoto, Luc Vinet, Alexei Zhedanov
TL;DR
This paper presents an infinite-dimensional representation of the rank 1 double affine Hecke algebra, leading to new orthogonal polynomials on the unit circle that are analogs of Askey-Wilson polynomials.
Contribution
It introduces a novel tridiagonal representation of the algebra and constructs new orthogonal polynomials on the circle and interval.
Findings
Polynomials are orthogonal on the unit circle.
Representation is naturally tridiagonal.
Polynomials are analogs of Askey-Wilson polynomials.
Abstract
An inifinite-dimensional representation of the double affine Hecke algebra of rank 1 and type 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.
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Taxonomy
TopicsMathematical functions and polynomials · Matrix Theory and Algorithms · Quantum chaos and dynamical systems