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

In this paper we classify all the irreducible super-unitary representations ofsu(p,q/n), which can be integrated up to a unitary representation ofS(U(p,q)×U(n)), a Lie group corresponding to the even part ofsu(p,q/n). Note that a real form of the Lie superalgebrasl(m/n;) which has non-trivial superunitary representations is of the formsu(p,q/n)(p+q=m) orsu(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.