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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…
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…