106 citations · 956 across the 40 of their papers we have counts for
12 papers · 1 filter
A superintegrable discrete harmonic oscillator based on bivariate Charlier polynomials
Vincent X. Genest, Hiroshi Miki, Luc Vinet +1
A simple discrete model of the two dimensional isotropic harmonic oscillator is presented. It is superintegrable with su(2) as its symmetry algebra. It is constructed with the help…
The Dirac-Dunkl operator and a higher rank Bannai-Ito algebra
Hendrik De Bie, Vincent X. Genest, Luc Vinet
The kernel of the Dirac-Dunkl operator is examined. The symmetry algebra of the associated Dirac-Dunkl equation on is determ…
An algebraic interpretation of the multivariate -Krawtchouk polynomials
Vincent X. Genest, Sarah Post, Luc Vinet
The multivariate quantum -Krawtchouk polynomials are shown to arise as matrix elements of "-rotations" acting on the state vectors of many -oscillators. The focus is put o…
Quantum spin chains with fractional revival
Vincent X. Genest, Luc Vinet, Alexei Zhedanov
A systematic study of fractional revival at two sites in quantum spin chains is presented and analytic models with this phenomenon are exhibited. The generic models have two e…
Exact Fractional Revival in Spin Chains
Vincent X. Genest, Luc Vinet, Alexei Zhedanov
The occurrence of fractional revival in quantum spin chains is examined. Analytic models where this phenomenon can be exhibited in exact solutions are provided. It is explained tha…
The non-symmetric Wilson polynomials are the Bannai-Ito polynomials
Vincent X. Genest, Luc Vinet, Alexei Zhedanov
The one-variable non-symmetric Wilson polynomials are shown to coincide with the Bannai-Ito polynomials. The isomorphism between the corresponding degenerate double affine Hecke al…
Tridiagonalization of the hypergeometric operator and the Racah-Wilson algebra
Vincent X. Genest, Mourad E. H. Ismail, Luc Vinet +1
The algebraic underpinning of the tridiagonalization procedure is investigated. The focus is put on the tridiagonalization of the hypergeometric operator and its associated quadrat…
Embeddings of the Racah Algebra into the Bannai-Ito Algebra
Vincent X. Genest, Luc Vinet, Alexei Zhedanov
Embeddings of the Racah algebra into the Bannai-Ito algebra are proposed in two realizations. First, quadratic combinations of the Bannai-Ito algebra generators in their standard r…
The equitable presentation of and a -analog of the Bannai-Ito algebra
Vincent X. Genest, Luc Vinet, Alexei Zhedanov
The equitable presentation of the quantum superalgebra , in which all generators appear on an equal footing, is exhibited. It is observed that in their equit…
A superintegrable discrete oscillator and two-variable Meixner polynomials
Julien Gaboriaud, Vincent X. Genest, Jessica Lemieux +1
A superintegrable, discrete model of the quantum isotropic oscillator in two-dimensions is introduced. The system is defined on the regular, infinite-dimensional $\mathbb{N}\times…
The quantum superalgebra and a -generalization of the Bannai-Ito polynomials
Vincent X. Genest, Luc Vinet, Alexei Zhedanov
The Racah problem for the quantum superalgebra is considered. The intermediate Casimir operators are shown to realize a -deformation of the Bannai-Ito…
A Dirac-Dunkl equation on and the Bannai-Ito algebra
Hendrik De Bie, Vincent X. Genest, Luc Vinet
The Dirac-Dunkl operator on the 2-sphere associated to the reflection group is considered. Its symmetries are found and are shown to generate the Bannai-Ito algebr…