On polynomial symmetry algebras underlying superintegrable systems in Darboux spaces
Ian Marquette,
Junze Zhang,
Yao-Zhong Zhang
Abstract:We review three different approaches to polynomial symmetry algebras underlying superintegrable systems in Darboux spaces. The first method consists of using deformed oscillator algebra to obtain finite-dimensional representations of quadratic algebras. This allow one to gain information on the spectrum of the superintegrable systems. The second method has similarities with the induced module construction approach in the context of Lie algebras and can be used to construct infinite dimensional representations … Show more
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