106 citations · 956 across the 40 of their papers we have counts for
48 papers
An embedding of the Bannai-Ito algebra in and polynomials
Pascal Baseilhac, Vincent X. Genest, Luc Vinet +1
An embedding of the Bannai-Ito algebra in the universal enveloping algebra of is provided. A connection with the characterization of the little Jacobi po…
and generalized Bannai-Ito algebras
vincent X. Genest, Luc Lapointe, Luc Vinet
Generalizations of the (rank 1) Bannai-Ito algebra are obtained from a refinement of the grade involution of the Lie super algebra . A hyperoctahedral extensio…
RG Flow from Theory to the 2D Ising Model
Nikhil Anand, Vincent X. Genest, Emanuel Katz +2
We study 1+1 dimensional theory using the recently proposed method of conformal truncation. Starting in the UV CFT of free field theory, we construct a complete basis of stat…
Coupling coefficients of and multivariate -Racah polynomials
Vincent X. Genest, Plamen Iliev, Luc Vinet
Gasper & Rahman's multivariate -Racah polynomials are shown to arise as connection coefficients between families of multivariate -Hahn or -Jacobi polynomials. The families…
A superintegrable model with reflections on and the higher rank Bannai-Ito algebra
Hendrik De Bie, Vincent X. Genest, Jean-Michel Lemay +1
A quantum superintegrable model with reflections on the -sphere is presented. Its symmetry algebra is identified with the higher rank generalization of the Bannai-Ito algebr…
Bannai-Ito algebras and the superalgebra
Hendrik De Bie, Vincent X. Genest, Wouter van de Vijver +1
The Bannai-Ito algebra of rank is defined as the algebra generated by the Casimir operators arising in the -fold tensor product of the superalgebra. Th…
A higher rank Racah algebra and the Laplace-Dunkl operator
Hendrik De Bie, Vincent X. Genest, Wouter van de Vijver +1
A higher rank generalization of the (rank one) Racah algebra is obtained as the symmetry algebra of the Laplace-Dunkl operator associated to the root system. This…
Supersymmetry of the quantum rotor
Vincent X. Genest, Luc Vinet, Guo-Fu Yu +1
The quantum rotor is shown to be supersymmetric. The supercharge , whose square equals the Hamiltonian, is constructed with reflection operators. The conserved quantities that c…
Persymmetric Jacobi matrices, isospectral deformations and orthogonal polynomials
Vincent X. Genest, Satoshi Tsujimoto, Luc Vinet +1
Persymmetric Jacobi matrices are invariant under reflection with respect to the anti-diagonal. The associated orthogonal polynomials have distinctive properties that are discussed.…
A superintegrable model with reflections on and the rank two Bannai-Ito algebra
Hendrik De Bie, Vincent X. Genest, Jean-Michel Lemay +1
A quantum superintegrable model with reflections on the three-sphere is presented. Its symmetry algebra is identified with the rank-two Bannai-Ito algebra. It is shown that the Ham…
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…
Two-variable Jacobi polynomials
Vincent X. Genest, Jean-Michel Lemay, Luc Vinet +1
A two-variable generalization of the Big Jacobi polynomials is introduced and characterized. These bivariate polynomials are constructed as a coupled product of two univariate…
The Bannai-Ito algebra and some applications
Hendrik De Bie, Vincent X. Genest, Satoshi Tsujimoto +2
The Bannai-Ito algebra is presented together with some of its applications. Its relations with the Bannai-Ito polynomials, the Racah problem for the algebra, a superin…