English

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

High Energy Physics - Theory 2009-10-28 v2 Quantum Algebra

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 Uq(su(1,1))U_q(su(1,1)) and type-I quantum superalgebras such as Uq(gl(11))U_q(gl(1|1)) and Uq(gl(21))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 qq. We develop a technique for constructing the corresponding spectral-dependent R-matrices. As examples we work out the the RR-matrices for the three quantum algebras mentioned above in certain representations.

Keywords

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

R2 v1 2026-07-22T15:50:03.942Z