Representations and Clebsch-Gordan coefficients for the Jordanian quantum algebra U_h(sl(2))

Abstract

Representation theory for the Jordanian quantum algebra $U=U_h(sl(2))$ is developed. Closed form expressions are given for the action of the generators of U on the basis vectors of finite dimensional irreducible representations. It is shown how representation theory of U has a close connection to combinatorial identities involving summation formulas. A general formula is obtained for the Clebsch-Gordan coefficients $C_{n_1,n_2,m}^{j_1,j_2,j}(h)$ of U. These Clebsch-Gordan coefficients are shown to coincide with those of su(2) for $n_1+n_2\le m$, but for $n_1+n_2>m$ they are in general a nonzero monomial in $h^{n_1+n_2-m}$.

LaTeX 2.09, 18 pages, no figures

References in corpus (1)

• Irreducible decomposition for tensor prodect representations of Jordanian quantum algebras

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