106 citations · 956 across the 40 of their papers we have counts for
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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…