A generalized Q-operator for U_q(S-frakturl₂) vertex models

In this paper, we construct a Q-operator as a trace of a representation of the universal A-matrix of U_q(S-frakturl₂) 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 three 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.