Classification of irreducible super-unitary representations of su(p,q/n)

In this paper we classify all the irreducible super unitary representations of su(p, q/n), which can be intergrated up to a unitary representation of S(U(p, q)xU(n)), a Lie group corresponding to the even part of su(p, q/n). Note that a real form of the Lie superalgebra sl(m/n: C) which has non-trivial superunitary representations is of the form su(p, q/n)(p+q=m) or su(m/r, s)(r+s=n). Moreover, we give an explicit realization for each irreducible super-unitary representation, using the oscillator representation of an orthosymplectic Lie superalgebra. (orig.)