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195 papers
The rank two Jacobi algebra
Nicolas Crampe, Satoshi Tsujimoto, Luc Vinet +1
The quadratic rank two Jacobi algebra is identified from the relations obeyed by the bispectral operators of the two variable Jacobi polynomials orthogonal on the triangle. It is s…
Eigenvalue equations for sieved polynomials or proving Askey right again
Luc Vinet, Alexei Zhedanov
The sieved Jacobi polynomials have been introduced by Askey. These can be obtained from conveniently taking to be a root of unity in the Askey-Wilson polynomials. The question…
Bispectrality of the sieved Jacobi polynomials
Luc Vinet, Alexei Zhedanov
It is shown that the CMV Laurent polynomials associated to the sieved Jacobi polynomials on the unit circle satisfy an eigenvalue equation with respect to a first order differentia…
The CMV bispectrality of the Jacobi polynomials on the unit circle
Luc Vinet, Alexei Zhedanov
We show that the Jacobi polynomials that are orthogonal on the unit circle (the Jacobi OPUC) are CMV bispectral. This means that the corresponding Laurent polynomials in the CMV ba…
Spectral surgery and high-fidelity quantum state transfer in chains
Luc Vinet, Alexei Zhedanov
We consider an inhomogeneous spin chain which interpolates between the Krawtchouk one with perfect state transfer and the homogeneous chain. This model can be used to per…
Meta Algebras and Biorthogonal Rational Functions: The Hahn Case
Satoshi Tsujimoto, Luc Vinet, Alexei Zhedanov
The finite families of biorthogonal rational functions and orthogonal polynomials of Hahn type are interpreted algebraically in a unified way by considering the three-generated met…