Publications (120)
The generalized Racah algebra as a commutant
Julien Gaboriaud, Luc Vinet, Stéphane Vinet +1
Dunkl shift operators and Bannai-Ito polynomials
Satoshi Tsujimoto, Luc Vinet, Alexei Zhedanov
The Quantum Dynamics of the Compactified Trigonometric Ruijsenaars-Schneider Model
Jan Felipe van Diejen, Luc Vinet
d-Orthogonal polynomials and su(2)
Vincent X. Genest, Luc Vinet, Alexei Zhedanov
A superintegrable finite oscillator in two dimensions with SU(2) symmetry
Hiroshi Miki, Sarah Post, Luc Vinet +1
A superintegrable discrete harmonic oscillator based on bivariate Charlier polynomials
Vincent X. Genest, Hiroshi Miki, Luc Vinet +1
Exact operator solution of the Calogero-Sutherland model
Luc Lapointe, Luc Vinet
A Rodrigues formula for the Jack polynomials and the Macdonald-Stanley conjecture
Luc Lapointe, Luc Vinet
Bannai-Ito algebras and the $osp(1,2)$ superalgebra
Hendrik De Bie, Vincent X. Genest, Wouter van de Vijver +1
On an integrable system related to the relativistic Toda lattice -Bäcklund transformation and integrable discretization
Luc Vinet, Guo-Fu Yu, Ying-Nan Zhang
A higher rank Racah algebra and the $\mathbb{Z}_2^{n}$ Laplace-Dunkl operator
Hendrik De Bie, Vincent X. Genest, Wouter van de Vijver +1
The q-Heun operator of big q-Jacobi type and the q-Heun algebra
Pascal Baseilhac, Luc Vinet, Alexei Zhedanov
Little and Big $q-$Jacobi Polynomials and the Askey-Wilson algebra
Pascal Baseilhac, Xavier Martin, Luc Vinet +1
Persymmetric Jacobi matrices, isospectral deformations and orthogonal polynomials
Vincent X. Genest, Satoshi Tsujimoto, Luc Vinet +1
The singular and the 2:1 anisotropic Dunkl oscillators in the plane
Vincent X. Genest, Luc Vinet, Alexei Zhedanov
Generalized Bochner theorem: characterization of the Askey-Wilson polynomials
Luc Vinet, Alexei Zhedanov
Generalized squeezed-coherent states of the finite one-dimensional oscillator and matrix multi-orthogonality
Vincent X. Genest, Luc Vinet, Alexei Zhedanov
Jordan algebras and orthogonal polynomials
Satoshi Tsujimoto, Luc Vinet, Alexei Zhedanov
The Dunkl oscillator in the plane II : representations of the symmetry algebra
Vincent X. Genest, Mourad E. H. Ismail, Luc Vinet +1
$\mathfrak {osp}(1,2)$ and generalized Bannai-Ito algebras
vincent X. Genest, Luc Lapointe, Luc Vinet
The equitable Racah algebra from three su(1,1) algebras
Vincent X. Genest, Luc Vinet, Alexei Zhedanov
An Algebraic Model for the Multiple Meixner Polynomials of the First Kind
Hiroshi Miki, Satoshi Tsujimoto, Luc Vinet +1
An algebraic interpretation of the continuous big q-Hermite polynomials
Roberto Floreanini, Jean LeTourneux, Luc Vinet
Dynamical Invariants and Berry's Phase for Generalized Driven Harmonic Oscillators
Barbara Sanborn, Sergei K. Suslov, Luc Vinet
Analytic next-to-nearest neighbour XX models with perfect state transfer and fractional revival
Matthias Christandl, Luc Vinet, Alexei Zhedanov
The Hahn superalgebra and supersymmetric Dunkl oscillator models
Vincent X. Genest, Jean-Michel Lemay, Luc Vinet +1
The Heun operator of Hahn type
Luc Vinet, Alexei Zhedanov
The multivariate Krawtchouk polynomials as matrix elements of the rotation group representations on oscillator states
Vincent X. Genest, Luc Vinet, Alexei Zhedanov
The algebra of dual -1 Hahn polynomials and the Clebsch-Gordan problem of sl_{-1}(2)
Vincent X Genest, Luc Vinet, Alexei Zhedanov
CMV matrices and little and big -1 Jacobi polynomials
Maxim Derevyagin, Luc Vinet, Alexei Zhedanov
The equitable presentation of $\mathfrak{osp}_q(1|2)$ and a $q$-analog of the Bannai-Ito algebra
Vincent X. Genest, Luc Vinet, Alexei Zhedanov
The Bannai-Ito polynomials as Racah coefficients of the sl_{-1}(2) algebra
Vincent X. Genest, Luc Vinet, Alexei Zhedanov
Rodrigues formulas for the Macdonald polynomials
Luc Lapointe, Luc Vinet
$SU_q(3)$ corepresentations and bivariate $q$-Krawtchouk polynomials
Geoffroy Bergeron, Erik Koelink, Luc Vinet
Double affine Hecke algebra of rank 1 and orthogonal polynomials on the unit circle
Satoshi Tsujimoto, Luc Vinet, Alexei Zhedanov
Coupling coefficients of $su_q(1,1)$ and multivariate $q$-Racah polynomials
Vincent X. Genest, Plamen Iliev, Luc Vinet
A superintegrable model with reflections on $S^3$ and the rank two Bannai-Ito algebra
Hendrik De Bie, Vincent X. Genest, Jean-Michel Lemay +1
Bargmann and Barut-Girardello models for the Racah algebra
Hendrik De Bie, Plamen Iliev, Luc Vinet
Coherent Transport in Photonic Lattices: A Survey of Recent Analytic Results
Ãric-Olivier Bossé, Luc Vinet
Generating functions for the osp(1|2) Clebsch-Gordan coefficients
Geoffroy Bergeron, Luc Vinet
A short proof of the integrality of the Macdonald (q,t)-Kostka coefficients
Luc Lapointe, Luc Vinet
The Dunkl oscillator in three dimensions
Vincent X. Genest, Luc Vinet, Alexei Zhedanov
$q$-Rotations and Krawtchouk polynomials
Vincent X. Genest, Sarah Post, Luc Vinet +2
A graph with fractional revival
Pierre-Antoine Bernard, Ada Chan, Ãrika Loranger +2
An algebraic interpretation of the $q$-Meixner polynomials
Julien Gaboriaud, Luc Vinet
An embedding of the Bannai-Ito algebra in $\mathcal{U}(\mathfrak{osp}(1,2))$ and $-1$ polynomials
Pascal Baseilhac, Vincent X. Genest, Luc Vinet +1
Tridiagonalization and the Heun equation
F. Alberto Grünbaum, Luc Vinet, Alexei Zhedanov
The Racah algebra and superintegrable models
Vincent X. Genest, Luc Vinet, Alexei Zhedanov
A limit $q=-1$ for the big q-Jacobi polynomials
Luc Vinet, Alexei Zhedanov
$q$--Hypergeometric Functions in the Formalism of Free Fields
Alexei Morozov, Luc Vinet
A "missing" family of classical orthogonal polynomials
Luc Vinet, Alexei Zhedanov
The dual pair $Pin(2n)\times\mathfrak{osp}(1|2)$, the Dirac equation and the Bannai-Ito algebra
Julien Gaboriaud, Luc Vinet, Stéphane Vinet +1
Para-Krawtchouk polynomials on a bi-lattice and a quantum spin chain with perfect state transfer
Luc Vinet, Alexei Zhedanov
A superintegrable model with reflections on $S^{n-1}$ and the higher rank Bannai-Ito algebra
Hendrik De Bie, Vincent X. Genest, Jean-Michel Lemay +1
-1 Krall-Jacobi Polynomials
Luc Vinet, Guo-Fu Yu, Alexei Zhedanov
The non-symmetric Wilson polynomials are the Bannai-Ito polynomials
Vincent X. Genest, Luc Vinet, Alexei Zhedanov
Non-Hermitian oscillator Hamiltonians and multiple Charlier polynomials
Hiroshi Miki, Luc Vinet, Alexei Zhedanov
Exact State Revival in a Spin Chain with Next-To-Nearest Neighbour Interactions
Matthias Christandl, Luc Vinet, Alexei Zhedanov
Bispectrality of the Complementary Bannai-Ito Polynomials
Vincent X. Genest, Luc Vinet, Alexei Zhedanov
Quasi-Linear Algebras and Integrability (the Heisenberg Picture)
Luc Vinet, Alexei Zhedanov
Tridiagonalization of the hypergeometric operator and the Racah-Wilson algebra
Vincent X. Genest, Mourad E. H. Ismail, Luc Vinet +1
Two-variable $-1$ Jacobi polynomials
Vincent X. Genest, Jean-Michel Lemay, Luc Vinet +1
The Generic Superintegrable System on the 3-Sphere and the $9j$ Symbols of $\mathfrak{su}(1,1)$
Vincent X. Genest, Luc Vinet
Quantum State Transfer in a Two-dimensional Regular Spin Lattice of Triangular Shape
Hiroshi Miki, Satoshi Tsujimoto, Luc Vinet +1
A Dirac-Dunkl equation on $S^2$ and the Bannai-Ito algebra
Hendrik De Bie, Vincent X. Genest, Luc Vinet
A $q$-generalization of the para-Racah polynomials
Jean-Michel Lemay, Luc Vinet, Alexei Zhedanov
Almost perfect state transfer in quantum spin chains
Luc Vinet, Alexei Zhedanov
A "Continuous" Limit of the Complementary Bannai-Ito Polynomials: Chihara Polynomials
Vincent X. Genest, Luc Vinet, Alexei Zhedanov
The quantum superalgebra $\mathfrak{osp}_{q}(1|2)$ and a $q$-generalization of the Bannai-Ito polynomials
Vincent X. Genest, Luc Vinet, Alexei Zhedanov
Families of superintegrable Hamiltonians constructed from exceptional polynomials
Sarah Post, Satoshi Tsujimoto, Luc Vinet
Free-Field Representation of Group Element for Simple Quantum Group
Alexei Morozov, Luc Vinet
Quantum spin chains with fractional revival
Vincent X. Genest, Luc Vinet, Alexei Zhedanov
Quantum Walks on Graphs of the Ordered Hamming Scheme and Spin Networks
Hiroshi Miki, Satoshi Tsujimoto, Luc Vinet
The multivariate Charlier polynomials as matrix elements of the Euclidean group representation on oscillator states
Vincent X. Genest, Hiroshi Miki, Luc Vinet +1
Dual -1 Hahn polynomials: "classical" polynomials beyond the Leonard duality
Satoshi Tsujimoto, Luc Vinet, Alexei Zhedanov
Interbasis expansions for the isotropic 3D harmonic oscillator and bivariate Krawtchouk polynomials
Vincent X. Genest, Luc Vinet, Alexei Zhedanov
Generating functions for the Bannai-Ito polynomials
Geoffroy Bergeron, Luc Vinet, Satoshi Tsujimoto
Hypergeometric Orthogonal Polynomials with respect to Newtonian Bases
Luc Vinet, Alexei Zhedanov
An infinite family of superintegrable Hamiltonians with reflection in the plane
Sarah Post, Luc Vinet, Alexei Zhedanov
How to construct spin chains with perfect state transfer
Luc Vinet, Alexei Zhedanov
The Dunkl-Coulomb problem in the plane
Vincent X. Genest, Andréanne Lapointe, Luc Vinet
The Dunkl oscillator in the plane I : superintegrability, separated wavefunctions and overlap coefficients
Vincent X. Genest, Mourad E. H. Ismail, Luc Vinet +1
From $sl_q(2)$ to a Parabosonic Hopf Algebra
Satoshi Tsujimoto, Luc Vinet, Alexei Zhedanov
Dual -1 Hahn polynomials and perfect state transfer
Luc Vinet, Alexei Zhedanov
Signal processing, orthogonal polynomials, and Heun equations
Geoffroy Bergeron, Luc Vinet, Alexei Zhedanov
Embeddings of the Racah Algebra into the Bannai-Ito Algebra
Vincent X. Genest, Luc Vinet, Alexei Zhedanov
An algebraic interpretation of the multivariate $q$-Krawtchouk polynomials
Vincent X. Genest, Sarah Post, Luc Vinet
Supersymmetry of the quantum rotor
Vincent X. Genest, Luc Vinet, Guo-Fu Yu +1
A model for the continuous q-ultraspherical polynomials
Roberto Floreanini, Luc Vinet
The multivariate Hahn polynomials and the singular oscillator
Vincent X. Genest, Luc Vinet
Fractional Revival and Association Schemes
Ada Chan, Gabriel Coutinho, Christino Tamon +2
The multivariate Meixner polynomials as matrix elements of $SO(d,1)$ representations on oscillator states
Vincent X. Genest, Hiroshi Miki, Luc Vinet +1
Quantum Fractional Revival on Graphs
Ada Chan, Gabriel Coutinho, Christino Tamon +2
Representations of the Schrödinger group and matrix orthogonal polynomials
Luc Vinet, Alexei Zhedanov
Creation operators for the Macdonald and Jack polynomials
Luc Lapointe, Luc Vinet
The $\mathbb{Z}_2^n$ Dirac-Dunkl operator and a higher rank Bannai-Ito algebra
Hendrik De Bie, Vincent X. Genest, Luc Vinet
A Quantum Analogue of the ${\cal Z}$ Algebra
A. Hamid Bougourzi, Luc Vinet
Algebraic Heun operator and band-time limiting
F. Alberto Grünbaum, Luc Vinet, Alexei Zhedanov
The Bannai-Ito algebra and a superintegrable system with reflections on the 2-sphere
Vincent X. Genest, Luc Vinet, Alexei Zhedanov
The para-Racah polynomials
Jean-Michel Lemay, Luc Vinet, Alexei Zhedanov