Colored solutions of the Yang–Baxter equation from representations of Uqgl(2)

Abstract

We study the Hopf algebra structure and the highest weight representation of a multiparameter version of Uqgl(2). The Hopf algebra maps of this algebra are explicitly given. We show that the multiparameter universal ℛ matrix can be constructed directly as a quantum double intertwiner without using Reshetikhin’s twisting transformation. We find there are two types highest weight representations for this algebra: type a corresponds to the qeneric q and type b corresponds to the case that q is a root of unity. When applying the representation theory to the multi-parameter universal ℛ matrix, both standard and nonstandard colored solutions of the Yang–Baxter equation are obtained.