dorsal/arxiv
View SchemaRepresentations and Clebsch-Gordan coefficients for the Jordanian quantum algebra U_h(sl(2))
| Authors | Joris Van der Jeugt |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9703011 |
| URL | https://arxiv.org/abs/q-alg/9703011 |
| DOI | 10.1088/0305-4470/31/5/017 |
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 $C^{j_1,j_2,j}_{n_1,n_2,m}(h)$ of U. These Clebsch-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 monomial in $h^{n_1+n_2-m}$.
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"abstract": "Representation theory for the Jordanian quantum algebra $U=U_h(sl(2))$ is\ndeveloped. Closed form expressions are given for the action of the generators\nof U on the basis vectors of finite dimensional irreducible representations. It\nis shown how representation theory of U has a close connection to combinatorial\nidentities involving summation formulas. A general formula is obtained for the\nClebsch-Gordan coefficients $C^{j_1,j_2,j}_{n_1,n_2,m}(h)$ of U. These\nClebsch-Gordan coefficients are shown to coincide with those of su(2) for\n$n_1+n_2 \\leq m$, but for $n_1+n_2 \u003e m$ they are in general a nonzero monomial\nin $h^{n_1+n_2-m}$.",
"arxiv_id": "q-alg/9703011",
"authors": [
"Joris Van der Jeugt"
],
"categories": [
"q-alg",
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"doi": "10.1088/0305-4470/31/5/017",
"title": "Representations and Clebsch-Gordan coefficients for the Jordanian quantum algebra U_h(sl(2))",
"url": "https://arxiv.org/abs/q-alg/9703011"
},
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