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Once More about Spectral-Dependent Quantum $R$-Matrix for $U_q(A_2)$

Anthony J. Bracken·Mark D. Gould·Yao-Zhong Zhang
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Abstract

The recently obtained results in \cite{ZG2} are used to compute the explicitly spectral-dependent $R$-matrix (or the intertwiners) on $V_{(6)}(x)\otimes V_{(6)}(y)$ and $V_{(3)}(x)\otimes V_{(6)}(y)$, where $V_{(6)}$ and $V_{(3)}$ are the 6-dimensional and fundamental representations of $U_q(A_2)$, respectively. It appears that the $R$-matrix on $V_{(3)}(x)\otimes V_{(6)}(y)$ depends on $q$ in the different way from what one might usually think: $q$ occurs in the $R$-matrix in fractional powers. It seems to be the first example in literatures of $R$-matrix with the new feature.

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Anthony J. Bracken, Mark D. Gould, Yao-Zhong Zhang. 1993-08-16. Once More about Spectral-Dependent Quantum $R$-Matrix for $U_q(A_2)$. https://arxiv.org/abs/hep-th/9308056

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