  We consider a realization of supersymmetric quantum mechanics where
supercharges are differential-difference operators with reflections. A
supersymmetric system with an extended Scarf I potential is presented and
analyzed. Its eigenfunctions are given in terms of little -1 Jacobi polynomials
which obey an eigenvalue equation of Dunkl type and arise as a q-> -1 limit of
the little q-Jacobi polynomials. Intertwining operators connecting the wave
functions of extended Scarf I potentials with different parameters are
presented.
