Irreducible Representations of Jordanian Quantum Algebra ${\mathcal{U}}_h(sl(2))$ Via a Nonlinear Map

Abstract

The generators of the Jordanian quantum algebra ${\mathcal{U}}_h(sl(2))$ are expressed as nonlinear invertible functions of the classical $sl(2)$ generators. This permits immediate explicit construction of the finite dimensional irreducible representations of the algebra ${\mathcal{U}}_h(sl(2))$. Using this construction, new finite dimensional solutions of the Yang-Baxter equation may be obtained.

10 pages, latex-file, references and some comments are added, version to be published in Mod. Phys. Lett

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