Solutions to the Quantum Yang-Baxter Equation with Extra Non-Additive Parameters
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 and type-I quantum superalgebras such as and are known to admit non-trivial one-parameter families of infinite-dimensional and finite dimensional irreps, respectively, even for generic . We develop a technique for constructing the corresponding spectral-dependent R-matrices. As examples we work out the the -matrices for the three quantum algebras mentioned above in certain representations.
Cite
@article{arxiv.hep-th/9405138,
title = {Solutions to the Quantum Yang-Baxter Equation with Extra Non-Additive Parameters},
author = {Anthony J. Bracken and Gustav W. Delius and Mark D. Gould and Yao-Zhong Zhang},
journal= {arXiv preprint arXiv:hep-th/9405138},
year = {2009}
}
Comments
13 pages