(2008-09-12) Kalnins, E.G.; Miller Jr., W.; Post, Sarah
We show how to construct realizations (models) of quadratic algebras for 2 dimensional second order superintegrable systems in terms of differential or difference operators in one variable.
We demonstrate how various models of the quantum algebras arise naturally from models of the Poisson algebras for the
corresponding classical superintegrable system. These techniques extend to quadratic algebras related to superintegrable systems in n dimensions and are intimately related to multivariable orthogonal polynomials.