%0 Journal Article
%T Recurrence approach and higher rank cubic algebras for the $N$-dimensional superintegrable systems
%A Md Fazlul Hoque
%A Ian Marquette
%A Yao-Zhong Zhang
%J Physics
%D 2015
%I arXiv
%X By applying the recurrence approach and coupling constant metamorphosis, we construct higher order integrals of motion for the Stackel equivalents of the $N$-dimensional superintegrable Kepler-Coulomb model with non-central terms and the double singular oscillators of type ($n, N-n$). We show how the integrals of motion generate higher rank cubic algebra $C(3)\oplus L_1\oplus L_2$ with structure constants involving Casimir operators of the Lie algebras $L_1$ and $L_2$. The realizations of the cubic algebras in terms of deformed oscillators enable us to construct finite dimensional unitary representations and derive the degenerate energy spectra of the corresponding superintegrable systems.
%U http://arxiv.org/abs/1511.03331v1