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arXiv · hep-th/9405138

Solutions to the Quantum Yang-Baxter Equation with Extra Non-Additive Parameters

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

We present a systematic technique to construct solutions to the Yang-Baxter equation which depend not only on a spectral parameter but in addition on further continuous parameters. These extra parameters enter the Yang-Baxter equation in a similar way to the spectral parameter but in a non-additive form. We exploit the fact that quantum non-compact algebras such as $U_q(su(1,1))$ and type-I quantum superalgebras such as $U_q(gl(1|1))$ and $U_q(gl(2|1))$ are known to admit non-trivial one-parameter families of infinite-dimensional and finite dimensional irreps, respectively, even for generic $q$. We develop a technique for constructing the corresponding spectral-dependent R-matrices. As examples we work out the the $R$-matrices for the three quantum algebras mentioned above in certain representations.

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Anthony J. Bracken, Gustav W. Delius, Mark D. Gould, Yao-Zhong Zhang. 1994-05-22. Solutions to the Quantum Yang-Baxter Equation with Extra Non-Additive Parameters. https://doi.org/10.1088/0305-4470%2F27%2F19%2F025

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