On Green endash Cusson Ansaetze and deformed supersymmetric quantum mechanics

Supersymmetric quantum mechanics cannot be deformed when the superposition of only a pair of usual bosons and fermions is considered, but it can if nontrivial parabosons and parafermions of the same order p of paraquantization are superposed. We take the simplest case p=2 and exhibit reducibility problems in that context by using Green endash Cusson Ansaetze following Macfarlane methods. Specific representations of the Lie superalgebra osp (2|2, R) play an interesting role in connection with possible deformations. copyright 1996 American Institute of Physics