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

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 $\mathcal{R}$ 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 $\mathcal{R}$ matrix, the so called standard and nonstandard colored solutions $R(\mu ,\nu ;{\mu }^{\prime },{\nu }^{\prime })$ of the Yang-Baxter equation is obtained.

[14]pages, latex, no figures

References in corpus (1)

• Bethe ansatz solution of a closed spin 1 XXZ Heisenberg chain with quantum algebra symmetry

Cited by in corpus (1)

• The coloured quantum plane