English

[Colored solutions of Yang-Baxter equation from representations of U_{q}gl(2)]

Mathematical Physics 2015-06-26 v1 math.MP

Abstract

We study the Hopf algebra structure and the highest weight representation of a multiparameter version of Uqgl(2)U_{q}gl(2). The commutation relations as well as other Hopf algebra maps are explicitly given. We show that the multiparameter universal R{\cal R} matrix can be constructed directly as a quantum double intertwiner, without using Reshetikhin's transformation. An interesting feature automatically appears in the representation theory: it can be divided into two types, one for generic qq, the other for qq being a root of unity. When applying the representation theory to the multiparameter universal R{\cal R} matrix, the so called standard and nonstandard colored solutions R(μ,ν;μ,ν)R(\mu,\nu; {\mu}', {\nu}') of the Yang-Baxter equation is obtained.

Keywords

Cite

@article{arxiv.math-ph/9911029,
  title  = {[Colored solutions of Yang-Baxter equation from representations of U_{q}gl(2)]},
  author = {[Pi-Gang Luan and H. C. Lee and R. B. Zhang]},
  journal= {arXiv preprint arXiv:math-ph/9911029},
  year   = {2015}
}

Comments

[14]pages, latex, no figures