Two-parametric deformation U-p,U-q[gl(2/1)] and its induce representations

The two-parametric quantum superalgebra U-p,U-q[gl(2/1)] is consistently defined. A construction procedure for induced representations of U-p,U-q[gl(2/1)] is described and allows us to construct explicitly all (typical and non-typical) finite-dimensional representations of this quantum superalgebra. In spite of some specific features, the present approach is similar to a previously developed method which, as shown here, is applicable not only to the one-parametric quantum deformations but also to the multi-parametric ones.