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

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

1993-07-02

arxiv.org/abs/hep-th/9307007v3

Lett.Math.Phys.31:101-110,1994

Physics

High Energy Physics

High Energy Physics - Theory

10 pages

Scientific paper

10.1007/BF00750144

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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