UNITARITY AND COMPLETE REDUCIBILITY OF CERTAIN MODULES OVER QUANTIZEDAFFINE LIE-ALGEBRAS

Let U(q)(g) denote the quantized affine Lie algebra and U(q)(g(1)) the quantized nontwisted affine Lie algebra. Let O(fin) be the category d efined in Sec. III. It is shown that when the deformation parameter q is not a root of unit all integrable representations of U(q)(g) in the category O(fin) are completely reducible and that every integrable ir reducible highest weight module over U(q)(g(1)) corresponding to q > 0 is equivalent to a unitary module.