Satoshi Tsujimoto, Luc Vinet, Alexei Zhedanov
Published 2017-09-21Version 1
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.
The polynomial representation of the double affine Hecke algebra of type $(C^\vee_n, C_n)$ for specialized parameters
On the basic representation of the double affine Hecke algebra at critical level
Quasi-polynomial representations of double affine Hecke algebras
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