  The Dunkl-Coulomb system in the plane is considered. The model is defined in
terms of the Dunkl Laplacian, which involves reflection operators, with a
$r^{-1}$ potential. The system is shown to be maximally superintegrable and
exactly solvable. The spectrum of the Hamiltonian is derived algebraically
using a realization of $\mathfrak{so}(2,1)$ in terms of Dunkl operators. The
symmetry operators generalizing the Runge-Lenz vector are constructed. On
eigenspaces of fixed energy, the invariance algebra they generate is seen to
correspond to a deformation of $\mathfrak{su}(2)$ by reflections. The exact
solutions are given as products of Laguerre polynomials and Dunkl harmonics on
the circle.
