106 citations · 956 across the 40 of their papers we have counts for
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The Dunkl oscillator in the plane I : superintegrability, separated wavefunctions and overlap coefficients
Vincent X. Genest, Mourad E. H. Ismail, Luc Vinet +1
The isotropic Dunkl oscillator model in the plane is investigated. The model is defined by a Hamiltonian constructed from the combination of two independent parabosonic oscillators…
The algebra of dual -1 Hahn polynomials and the Clebsch-Gordan problem of sl_{-1}(2)
Vincent X Genest, Luc Vinet, Alexei Zhedanov
The algebra H of the dual -1 Hahn polynomials is derived and shown to arise in the Clebsch-Gordan problem of sl_{-1}(2). The dual -1 Hahn polynomials are the bispectral polynomials…
The Bannai-Ito polynomials as Racah coefficients of the sl_{-1}(2) algebra
Vincent X. Genest, Luc Vinet, Alexei Zhedanov
The Bannai-Ito polynomials are shown to arise as Racah coefficients for sl_{-1}(2). This Hopf algebra has four generators including an involution and is defined with both commutati…
Generalized squeezed-coherent states of the finite one-dimensional oscillator and matrix multi-orthogonality
Vincent X. Genest, Luc Vinet, Alexei Zhedanov
A set of generalized squeezed-coherent states for the finite u(2) oscillator is obtained. These states are given as linear combinations of the mode eigenstates with amplitudes dete…