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A quantum superintegrable model with reflections on the 2-sphere is introduced.
Quantum Field Theory and Parastatistics
Y. Ohnuki and S. Kamefuchi · 1982
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Algebraic Combinatorics I: Association Schemes
E. Bannai and T. Ito · 1984
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Irreducible representations of a graded Lie algebra
M.F. Gorodnii and G.B. Podkolzin · 1984
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Differential-difference operators associated to reflection groups
C. F. Dunkl · 1989
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“Hidden symmetry” of Askey-Wilson polynomials
A. Zhedanov · 1991
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Exact operator solution of the Calogero-Sutherland model
L. Lapointe and L. Vinet · 1996
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Symmetric functions and Hall polynomials
I. G. Macdonald · 1999
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Orthogonal Polynomials of Several Variables
C. F. Dunkl and Y. Xu · 2001
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Fractional helicity, Lorentz symmetry breaking, compactification and anyons
S. M. Klishevich, M. S. Plyushchay, and M. R. de Traubenberg · 2001
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The anticommutator spin algebra, its representations and quantum group invariance
M. Arik and U. Kayserilioglu · 2003
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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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Finite oscillator models: the Hahn oscillator
E. I. Jafarov, N. I. Stoilova, and J. Van der Jeugt · 2011
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Two-variable Wilson polynomials and the generic superintegrable system on the 3-sphere
E. G. Kalnins, W. Miller, and S. Post · 2011
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An infinite family of superintegrable Hamiltonians with reflection in the plane
S. Post, L. Vinet, and A. Zhedanov · 2011
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Supersymmetric Quantum Mechanics with reflections
S. Post, L. Vinet, and A. Zhedanov · 2011
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From s l q ( 2 ) sl_{q}(2) to a parabosonic Hopf algebra
S. Tsujimoto, L. Vinet, and A. Zhedanov · 2011
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Jordan algebra and orthogonal polynomials
S. Tsujimoto, L. Vinet, and A. Zhedanov · 2011
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A Bochner Theorem for Dunkl polynomials
L. Vinet and A. Zhedanov · 2011
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The Dunkl oscillator in three dimensions
V. X. Genest, L. Vinet, and A. Zhedanov · 2013
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The Racah algebra and superintegrable models
V. X. Genest, L. Vinet, and A. Zhedanov · 2013
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The Dunkl oscillator in the plane: I. Superintegrability, separated wavefunctions and overlap coefficients
V.X. Genest, M.E.H. Ismail, L. Vinet, and A. Zhedanov · 2013
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The Dunkl oscillator in the plane: II. Representations of the symmetry algebra
V.X. Genest, M.E.H. Ismail, L. Vinet, and A. Zhedanov · 2013
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Bispectrality of the Complementary Bannai–Ito polynomials
V.X. Genest, L. Vinet, and A. Zhedanov · 2013
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Superintegrability in two dimensions and the Racah-Wilson algebra
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A ‘missing’ family of classical orthogonal polynomials
L. Vinet and A. Zhedanov · 2011
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Mathematical Methods for Physicists
G. B. Arfken, H. Weber, and F. E. Harris · 2012
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Dunkl shift operators and Bannai–Ito polynomials
S. Tsujimoto, L. Vinet, and A. Zhedanov · 2012
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A limit q = − 1 q=-1 for the Big q q -Jacobi polynomials
L. Vinet and A. Zhedanov · 2012
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The Hahn superalgebra and supersymmetric Dunkl oscillator models
V. X. Genest, J-M. Lemay, L. Vinet, and A. Zhedanov · 2013
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A Laplace-Dunkl equation on S 2 S^{2} and the Bannai–Ito algebra
V. X. Genest, L. Vinet, and A. Zhedanov · 2013
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V.X. Genest, L. Vinet, and A. Zhedanov · 2013
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The singular and 2:1 anisotropic Dunkl oscillators in the plane
V.X. Genest, L. Vinet, and A. Zhedanov · 2013
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Contractions of 2D 2 nd order quantum superintegrable systems and the Askey scheme for hypergeometric orthogonal polynomials
E.G. Kalnins, W. Miller, and S. Post · 2013
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Classical and quantum superintegrability with applications
W. Miller, S. Post, and P. Winternitz · 2013
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Dual − 1 -1 Hahn polynomials: “Classical” polynomials beyond the Leonard duality
S. Tsujimoto, L. Vinet, and A. Zhedanov · 2013
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A ”continuous” limit of the Complementary Bannai-Ito polynomials: Chihara polynomials
V. X. Genest, L. Vinet, and A. Zhedanov · 2014
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The Bannai-Ito polynomials as Racah coefficients of the s l − 1 ( 2 ) sl_{-1}(2) algebra
V.X. Genest, L. Vinet, and A. Zhedanov · 2014
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