A Q-ANALOG OF THE SUPERSYMMETRIC OSCILLATOR AND ITS Q-SUPERALGEBRA

A q-analogue of the supersymmetric oscillator is constructed out of q-boson and q-fermion creation and annihilation operators. For a fixed n(B) + n(F) = 2n, (where n(B) and n(F) are q-boson and q-fermion occupation numbers, the irreducible representations of the q-superalgebra generated by the q-oscillator are (2n + 1)-dimensional. Particular cases when q is a root of +/- 1 are discussed. A realization of the quantum group SU(q)(2) is obtained using a pair of 1-fermion creation and annihilation operators.