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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…
Tridiagonal representations of the q-oscillator algebra and Askey-Wilson polynomials
Satoshi Tsujimoto, Luc Vinet, Alexei Zhedanov
A construction is given of the most general representations of the q-oscillator algebra where both generators are tridiagonal. It is shown to be connected to the Askey-Wilson polyn…
The Onsager algebra and multivariable special functions
Pascal Baseilhac, Luc Vinet, Alexei Zhedanov
Two sets of mutually commuting difference operators and , such that and generate a homomorphic image of the Onsager algebra for each $…
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…
An algebraic interpretation of the -Meixner polynomials
Julien Gaboriaud, Luc Vinet
An algebraic interpretation of the -Meixner polynomials is obtained. It is based on representations of on -oscillator states with the poly…
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…