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Representation theory for the Jordanian quantum algebra $U=U_h(sl(2))$ isdeveloped. Closed form expressions are given for the action of the generatorsof U on the basis vectors of finite dimensional irreducible representations. Itis shown how representation theory of U has a close connection to combinatorialidentities involving summation formulas. A general formula is obtained for theClebsch-Gordan coefficients $C^{j_1,j_2,j}_{n_1,n_2,m}(h)$ of U. TheseClebsch-Gordan coefficients are shown to coincide with those of su(2) for$n_1+n_2 \leq m$, but for $n_1+n_2 > m$ they are in general a nonzero monomialin $h^{n_1+n_2-m}$.Comment: LaTeX 2.09, 18 pages, no figure

Representations and Clebsch-Gordan coefficients for the Jordanian quantum algebra