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A supersymmetric extension of the Hahn algebra is introduced. This quadraticsuperalgebra, which we call the Hahn superalgebra, is constructed using therealization provided by the Dunkl oscillator model in the plane, whoseHamiltonian involves reflection operators. In this realization, the reflectionsact as grading operators and the odd generators are part of the Schwinger-Dunklalgebra, 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 andsatisfy the Hahn algebra supplemented with involutions. A family ofsupersymmetric Dunkl oscillator models in n dimensions is also considered. TheHamiltonians of these supersymmetric models differ from ordinary Dunkloscillators by pure reflection terms. In two dimensions, the supersymmetricDunkl oscillator is seen to have the even part of the Hahn superalgebra asinvariance algebra.

The Hahn superalgebra and supersymmetric Dunkl oscillator models