106 citations · 956 across the 40 of their papers we have counts for
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A Laplace-Dunkl equation on and the Bannai-Ito algebra
Vincent X. Genest, Luc Vinet, Alexei Zhedanov
The analysis of the Laplace-Dunkl equation on the -sphere is cast in the framework of the Racah problem for the Hopf algebra . The related Dunkl-L…
The Racah algebra and superintegrable models
Vincent X. Genest, Luc Vinet, Alexei Zhedanov
The universal character of the Racah algebra will be illustrated by showing that it is at the center of the relations between the Racah polynomials, the recoupling of three su(1,1)…
The Dunkl oscillator in three dimensions
Vincent X. Genest, Luc Vinet, Alexei Zhedanov
The isotropic Dunkl oscillator model in three-dimensional Euclidean space is considered. The system is shown to be maximally superintegrable and its symmetries are obtained by the…
The multivariate Meixner polynomials as matrix elements of representations on oscillator states
Vincent X. Genest, Hiroshi Miki, Luc Vinet +1
The multivariate Meixner polynomials are shown to arise as matrix elements of unitary representations of the group on oscillator states. These polynomials depend on d…
A "Continuous" Limit of the Complementary Bannai-Ito Polynomials: Chihara Polynomials
Vincent X. Genest, Luc Vinet, Alexei Zhedanov
A novel family of orthogonal polynomials called the Chihara polynomials is characterized. The polynomials are obtained from a "continuous" limit of the complementary Bannai-It…
The equitable Racah algebra from three su(1,1) algebras
Vincent X. Genest, Luc Vinet, Alexei Zhedanov
The Racah algebra, a quadratic algebra with two independent generators, is central in the analysis of superintegrable models and encodes the properties of the Racah polynomials. It…
The Hahn superalgebra and supersymmetric Dunkl oscillator models
Vincent X. Genest, Jean-Michel Lemay, Luc Vinet +1
A supersymmetric extension of the Hahn algebra is introduced. This quadratic superalgebra, which we call the Hahn superalgebra, is constructed using the realization provided by the…
Superintegrability in two dimensions and the Racah-Wilson algebra
Vincent X. Genest, Luc Vinet, Alexei Zhedanov
The analysis of the most general second-order superintegrable system in two dimensions: the generic 3-parameter model on the 2-sphere, is cast in the framework of the Racah problem…
Interbasis expansions for the isotropic 3D harmonic oscillator and bivariate Krawtchouk polynomials
Vincent X. Genest, Luc Vinet, Alexei Zhedanov
An explicit expression for the general bivariate Krawtchouk polynomials is obtained in terms of the standard Krawtchouk and dual Hahn polynomials. The bivariate Krawtchouk polynomi…
The multivariate Krawtchouk polynomials as matrix elements of the rotation group representations on oscillator states
Vincent X. Genest, Luc Vinet, Alexei Zhedanov
An algebraic interpretation of the bivariate Krawtchouk polynomials is provided in the framework of the 3-dimensional isotropic harmonic oscillator model. These polynomials in two…
The singular and the 2:1 anisotropic Dunkl oscillators in the plane
Vincent X. Genest, Luc Vinet, Alexei Zhedanov
Two Dunkl oscillator models are considered: one singular and the other with a 2:1 frequency ratio. These models are defined by Hamiltonians which include the reflection operators i…
The Dunkl oscillator in the plane II : representations of the symmetry algebra
Vincent X. Genest, Mourad E. H. Ismail, Luc Vinet +1
The superintegrability, wavefunctions and overlap coefficients of the Dunkl oscillator model in the plane were considered in the first part. Here finite-dimensional representations…