Finite-dimensional irreducible representations of the quantum superalgebraU q [gl(n/1)]

It is shown that every finite-dimensional irreducible module over the general linear Lie superalgebragl(n/1) can be deformed to an irreducible module ofU _q gl(n/1)], aq-analogue of the universal enveloping algebra ofgl(n/1). The results are extended also to all Kac modules, which in the atypical cases remain indecomposible. Within each module expressions for the transformations of the Gel'fand-Zetlin basis under the action of the algebra generators are written down. An analogoue of the Poincaré-Birkhoff-Witt theorem is formulated.