Superintegrability on the Dunkl oscillator model in three-dimensional spaces of constant curvature

In this paper, three-dimensional Dunkl oscillator models are studied in a generalized form of superintegrable Euclidean Hamiltonian systems to curved ones. These defined based on Hamiltonians, which depend deformation parameter underlying space and involve reflection operators. The corresponding symmetries obtained by the Jordan–Schwinger representations family Cayley–Klein orthogonal algebras using creation annihilation operators dynamical sl−1(2) algebra one-dimensional oscillator. resulting is soκ1κ2(4) with reflections, known as Jordan–Schwinger–Dunkl jsdκ1κ2(4). Hence, it shown that model maximally superintegrable. On other hand, superintegrability from viewpoint factorization approach. spectrum system derived through separation variables geodesic polar coordinates, eigenfunctions algebraically given terms Jacobi polynomials.