Finite dimensional representations of the quantum analog of the enveloping algebra of a complex simple Lie algebra

Let {Mathematical expression} be a complex simple Lie algebra. We show that when t is not a root of 1 all finite dimensional representations of the quantum analog U_t {Mathematical expression} are completely reducible, and we classify the irreducible ones in terms of highest weights. In particular, they can be seen as deformations of the representations of the (classical)U {Mathematical expression}.