  Representation theory for the Jordanian quantum algebra U=U_h(sl(2)) is
developed using a nonlinear relation between its generators and those of sl(2).
Closed form expressions are given for the action of the generators of U on the
basis vectors of finite dimensional irreducible representations. In the tensor
product of two such representations, a new basis is constructed on which the
generators of U have a simple action. Using this basis, a general formula is
obtained for the Clebsch-Gordan coefficients of U. It is shown that the
Clebsch-Gordan matrix is essentially the product of a triangular matrix with an
su(2) Clebsch-Gordan matrix. Using this fact, some remarkable properties of
these Clebsch-Gordan coefficients are derived.
