Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 7 (2011), 036, 20 pages      arXiv:1104.0734      https://doi.org/10.3842/SIGMA.2011.036
Contribution to the Special Issue “Symmetry, Separation, Super-integrability and Special Functions (S4)”

Models of Quadratic Algebras Generated by Superintegrable Systems in 2D

Sarah Post
Centre de Recherches Mathématiques, Université de Montréal, C.P. 6128 succ. Centre-Ville, Montréal (QC) H3C 3J7, Canada

Received February 01, 2011, in final form March 24, 2011; Published online April 05, 2011

Abstract
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.

Key words: quadratic algebras; superintegrability; special functions; representation theory.

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