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

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

1994-05-21

arxiv.org/abs/hep-th/9405138v2

J.Phys. A27 (1994) 6551-6562

Physics

High Energy Physics

High Energy Physics - Theory

13 pages

Scientific paper

10.1088/0305-4470/27/19/025

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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