Induced representations of the multiparameter Hopf superalgebras U(u)q(gl(m/n)) and U-uq(sl(m/n))

We construct the induced holomorphic representations of the multiparameter Hopf superalgebras U-uq(gl(m/n)) and U-uq(sl(m/n)). The first superalgebra we constructed earlier as the dual of the multiparameter quantum deformatio n of the supergroup GL(m/n). The second superalgebra is a Hopf subalgebra o f the first for a special choice of the parameters. The representations are labelled by m + n integer numbers, respectively m + n - 1 complex numbers, and act in the space of formal power series of (m + n)(m + n - 1)/2 non-co mmuting variables, of which mn are odd and the rest are even. These variabl es generate a q-deformation of a flag supermanifold of the supergroup GL(m/ n), respectively SL(m/n).