  The isotropic Dunkl oscillator model in three-dimensional Euclidean space is
considered. The system is shown to be maximally superintegrable and its
symmetries are obtained by the Schwinger construction using the
raising/lowering operators of the dynamical sl_{-1}(2) algebra of the
one-dimensional Dunkl oscillator. The invariance algebra generated by the
constants of motion, an extension of u(3) with reflections, is called the
Schwinger-Dunkl algebra sd(3). The system is shown to admit separation of
variables in Cartesian, polar (cylindrical) and spherical coordinates and the
corresponding separated solutions are expressed in terms of generalized
Hermite, Laguerre and Jacobi polynomials.
