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arXiv · hep-th/9307007

Quantum Affine Algebras and Universal $R$-Matrix with Spectral Parameter

Yao-Zhong Zhang·Mark D. Gould
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Abstract

Using the previous obtained universal $R$-matrix for the quantized nontwisted affine Lie algebras $U_q(A_1^{(1)})$ and $U_q(A_2^{(1)})$, we determine the explicitly spectral-dependent universal $R$-matrix for the corresponding quantum Lie algebras $U_q(A_1)$ and $U_q(A_2)$. As their applications, we reproduce the well-known results in the fundamental representations and we also derive an extreamly explicit formula of the spectral-dependent $R$-matrix for the adjoint representation of $U_q(A_2)$, the simplest non-trival case when the tensor product decomposition of the representation with itself has finite multiplicity.

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Yao-Zhong Zhang, Mark D. Gould. 1993-12-15. Quantum Affine Algebras and Universal $R$-Matrix with Spectral Parameter. https://doi.org/10.1007/bf00750144

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