BOSON-FERMION MODELS FOR OSP(1,2) AND UQ[OSP(1,2)]

A reducible representation of the simple Lie superalgebra osp(1,2) is constructed from two pairs of boson and one pair of fermion creation a nd annihilation operators. The representation contains in direct sum e very distinct (up to equivalence), finite-dimensional, irreducible rep resentation of osp(1,2) exactly once and so defines a model, generaliz ing to osp(1,2) Schwinger's boson model of su(2). The model of osp(1,2 ) is further generalized to a model of the quantum superalgebra U(q)[o sp(1,2)] in the case that q is not a root of unity. Matrix elements of generators and basic properties of the R matrix, known from previous studies, are rederived using the boson-fermion calculus.