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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…
Spin lattices, state transfer and bivariate Krawtchouk polynomials
Vincent X. Genest, Hiroshi Miki, Luc Vinet +1
The quantum state transfer properties of a class of two-dimensional spin lattices on a triangular domain are investigated. Systems for which the 1-excitation dynamics is exactly so…
-Rotations and Krawtchouk polynomials
Vincent X. Genest, Sarah Post, Luc Vinet +2
An algebraic interpretation of the one-variable quantum -Krawtchouk polynomials is provided in the framework of the Schwinger realization of involving…
The multivariate Hahn polynomials and the singular oscillator
Vincent X. Genest, Luc Vinet
Karlin and McGregor's d-variable Hahn polynomials are shown to arise in the (d+1)-dimensional singular oscillator model as the overlap coefficients between bases associated to the…
The Dunkl-Coulomb problem in the plane
Vincent X. Genest, Andréanne Lapointe, Luc Vinet
The Dunkl-Coulomb system in the plane is considered. The model is defined in terms of the Dunkl Laplacian, which involves reflection operators, with a potential. The syste…