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Models of Quadratic Algebras Generated by Superintegrable Systems in 2D
Symmetry, integrability and geometry: methods and applications, Tome 7 (2011) Cet article a éte moissonné depuis la source Math-Net.Ru

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In this paper, we consider operator realizations of quadratic algebras generated by second-order superintegrable systems in 2D. At least one such realization is given for each set of Stäckel equivalent systems for both degenerate and nondegenerate systems. In almost all cases, the models can be used to determine the quantization of energy and eigenvalues for integrals associated with separation of variables in the original system.
Keywords: quadratic algebras; superintegrability; special functions; representation theory. 
@article{SIGMA_2011_7_a35,
     author = {Sarah Post},
     title = {Models of {Quadratic} {Algebras} {Generated} by {Superintegrable} {Systems} {in~2D}},
     journal = {Symmetry, integrability and geometry: methods and applications},
     year = {2011},
     volume = {7},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2011_7_a35/}
}
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Sarah Post. Models of Quadratic Algebras Generated by Superintegrable Systems in 2D. Symmetry, integrability and geometry: methods and applications, Tome 7 (2011). http://geodesic.mathdoc.fr/item/SIGMA_2011_7_a35/

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