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arxiv: math-ph/9911029 · v1 · pith:PXKOVVLMnew · submitted 1999-11-23 · 🧮 math-ph · math.MP

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

classification 🧮 math-ph math.MP
keywords multiparameterrepresentationalgebracoloredequationhopfmatrixother
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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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