A Generalized Q-operator for Uq(ŝl2) Vertex Models

In this paper, we construct a Q-operator as a trace of a representation of the universal R-matrix of Uq(ŝl2 ) over an infinite-dimensional auxiliary space. This auxiliary space is a four-parameter generalization of the q-oscillator representations used previously. We derive generalized T -Q relations in which 3 of these parameters shift. After a suitable restriction of parameters, we give an explicit expression for the Q-operator of the 6-vertex model and show the connection with Baxter’s expression for the central block of his corresponding operator.