V
Vincent X. Genest
Researcher at Massachusetts Institute of Technology
Publications - 94
Citations - 1953
Vincent X. Genest is an academic researcher from Massachusetts Institute of Technology. The author has contributed to research in topics: Orthogonal polynomials & Hahn polynomials. The author has an hindex of 26, co-authored 94 publications receiving 1669 citations. Previous affiliations of Vincent X. Genest include Centre de Recherches Mathématiques & Université de Montréal.
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Superintegrability in Two Dimensions and the Racah–Wilson Algebra
TL;DR: The analysis of the generic 3-parameter superintegrable system in two dimensions has been studied in this article, where the Hamiltonian of the system and the generators of its quadratic symmetry algebra are shown to correspond to the total and intermediate Casimir operators of the combination of three \({\mathfrak{su}(1,1)}\) algebras, respectively.
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The Dunkl oscillator in the plane I : superintegrability, separated wavefunctions and overlap coefficients
TL;DR: The Schwinger-Dunkl algebra as mentioned in this paper is an extension of the Lie algebra with involutions that admits separation of variables in both Cartesian and polar coordinates, and the separated wavefunctions are respectively expressed in terms of generalized Hermite polynomials and products of Jacobi and Laguerre polynomorphisms.
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The Dunkl Oscillator in the Plane II: Representations of the Symmetry Algebra
TL;DR: In this paper, the superintegrability, wavefunctions and overlap coefficients of the Dunkl oscillator model in the plane were considered. But the authors focused on the symmetry algebra sd(2), which has six generators, including two involutions and a central element, and can be seen as a deformation of the Lie algebra.
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A Laplace-Dunkl Equation on S 2 and the Bannai-Ito Algebra
TL;DR: In this paper, the analysis of the Laplace-Dunkl equation on the 2-sphere is cast in the framework of the Racah problem for the Hopf algebra sl−1(2).
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The Dunkl oscillator in the plane I : superintegrability, separated wavefunctions and overlap coefficients
TL;DR: The Schwinger-Dunkl algebra as mentioned in this paper is an extension of the Lie algebra u(2) with involutions that admits separation of variables in both Cartesian and polar coordinates, and its symmetry generators are obtained by the Schwinger construction using parabosonic creation/annihilation operators.