  A supersymmetric extension of the Hahn algebra is introduced. This quadratic
superalgebra, which we call the Hahn superalgebra, is constructed using the
realization provided by the Dunkl oscillator model in the plane, whose
Hamiltonian involves reflection operators. In this realization, the reflections
act as grading operators and the odd generators are part of the Schwinger-Dunkl
algebra, which is a two-parameter extension of the bosonic su(2) construction.
The even part of the algebra is built from bilinears in the odd generators and
satisfy the Hahn algebra supplemented with involutions. A family of
supersymmetric Dunkl oscillator models in n dimensions is also considered. The
Hamiltonians of these supersymmetric models differ from ordinary Dunkl
oscillators by pure reflection terms. In two dimensions, the supersymmetric
Dunkl oscillator is seen to have the even part of the Hahn superalgebra as
invariance algebra.
