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The analysis of the most general second-order superintegrable system in two dimensions: the generic 3-parameter model on the 2-sphere, is cast in the framework of the Racah problem for the su(1,1) algebra.
On higher symmetries in quantum mechanics
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Nature of the symmetry group of the
Y. Granovskii and A. Zhedanov · 1988
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Exactly solved problems and their quadratic algebras (in Russian)
Y. Granovskii and A. Zhedanov · 1989
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Dynamical symmetry of anisotropic singular oscillator
O.F. Gal’bert, Y. Granovskii, and A. Zhedanov · 1991
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Quadratic algebra as a ‘hidden’ symmetry of the Hartmann potential
Y. Granovskii and A. Zhedanov · 1991
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Representations of Lie groups and Special Functions
N.J. Vilenkin and A.U. Klimyk · 1991
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Hidden symmetry of Askey-Wilson polynomials
A. Zhedanov · 1991
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Mutual integrability, quadratic algebras and dynamical symmetry
Y. Granovskii, A. Zhedanov, and I. Lutsenko · 1992
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Quadratic algebras and dynamics in curved spaces I. Oscillator
Y. Granovskii, A. Zhedanov, and I. Lutsenko · 1992
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Quadratic algebras and dynamics in curved spaces II. The Kepler problem
Y. Granovskii, A. Zhedanov, and I. Lutsenko · 1992
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Quadrics on Riemannian spaces of constant curvature. Separation of variables and connection with the Gaudin magnet
V.B. Kuznetsov · 1992
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Applications of Lie groups to differential equations
P. J. Olver · 1993
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Hidden symmetry algebra and overlap coefficients for two ring-shaped potentials
A. Zhedanov · 1993
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Superintegrable Systems: Polynomial Algebras and Quasi-Exactly Solvable Hamiltonians
P. Létourneau and L. Vinet · 1995
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Superintegrability and associated polynomial solutions: Euclidean space and the sphere in two dimensions
Superintegrability in classical and quantum systems
P. Tempesta, P. Winternitz, W. Miller, and G. Pogosyan, editors · 2005
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Unified treatment and classification of superintegrable systems with integrals quadratic in momenta on a two dimensonal manifold
C. Daskaloyannis and K. Ypsilantis · 2006
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Wilson function transforms related to Racah coefficients
W. Groenevelt · 2006
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Wilson polynomials and the generic superintegrable system on the 2-sphere
E.G. Kalnins, W. Miller, and S. Post · 2007
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Hypergeometric orthogonal polynomials and their q q -analogues
R. Koekoek, P.A. Lesky, and R.F. Swarttouw · 2010
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Two-Variable Wilson Polynomials and the Generic Superintegrable System on the 3-Sphere
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Completeness of multiseparable superintegrability on the complex 2-sphere
E.G. Kalnins, W. Miller, and G. Pogosyan · 2000
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Spectral properties of operators using tridiagonalization
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The classification of Leonard triples of Racah type
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Racah algebra realizations
V.X. Genest, L. Vinet, and A. Zhedanov · 2013
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E.G. Kalnins, W. Miller, and S. Post · 2013
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