N ov 1 99 9 ( July , 1999 ) 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 Uqgl(2). The commutation relations as well as other Hopf algebra maps are explicitly given. We show that the multiparameter universal 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 R matrix, the so called standard and nonstandard colored solutions R(μ, ν;μ, ν ) of the Yang-Baxter equation is obtained.