Factorization of the Universal R-matrix for $U_q({\widehat{sl}}_2)$

Abstract

The factorization of the universal R-matrix corresponding to so called Drinfeld Hopf structure is described on the example of quantum affine algebra $U_q({\widehat{sl}}_2)$. As a result of factorization procedure we deduce certain differential equations on the factors of the universal $\mathcal{R}$-matrix, which allow to construct uniquely these factors in the integral form.

28 pages, LaTeX 2.09 using amssym.def and amssym.tex

References in corpus (7)

• Braid Group Action and Quantum Affine Algebras
• Macdonald's Evaluation Conjectures and Difference Fourier Transform
• Elliptic quantum groups $E_{\tau ,\eta }(s{l}_2)$ and quasi-Hopf algebras
• Gauss decomposition of trigonometric R-matrices
• Quasi-Hopf algebras associated with sl(2) and complex curves
• Elliptic algebra $A_{q,p}(\widehat{s{l}_2})$ in the scaling limit
• Zeros and poles of quantum current operators and the condition of quantum integrability

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• Shifted quantum groups and matter multiplets in supersymmetric gauge theories
• On the R-matrix realization of quantum loop algebras
• Weight function for the quantum affine algebra $U_q(A_2^{(2)})$
• Quantizing the discrete Painlevé VI equation : The Lax formalism