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

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

1999-11-23

arxiv.org/abs/math-ph/9911029v1

Physics

Mathematical Physics

[14]pages, latex, no figures

Scientific paper

We study the Hopf algebra structure and the highest weight representation of a multiparameter version of $U_{q}gl(2)$. The commutation relations as well as other Hopf algebra maps are explicitly given. We show that the multiparameter universal ${\cal R}$ 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 $q$, the other for $q$ being a root of unity. When applying the representation theory to the multiparameter universal ${\cal R}$ matrix, the so called standard and nonstandard colored solutions $R(\mu,\nu; {\mu}', {\nu}')$ of the Yang-Baxter equation is obtained.

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