A q-analogue 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 nB+nF=2n, (where nB and nF 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 +or-1 are discussed. A realization of the quantum group SUq(2) is obtained using a pair of 1-fermion creation and annihilation operators.