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

[Pi-Gang Luan·H. C. Lee·R. B. Zhang]
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Abstract

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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[Pi-Gang Luan, H. C. Lee, R. B. Zhang]. 1999-11-23. [Colored solutions of Yang-Baxter equation from representations of U_{q}gl(2)]. https://doi.org/10.1063/1.1287435

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