A Generalized Q-operator for U_q(\hat(sl_2)) Vertex Models

TL;DR

This paper introduces a generalized Q-operator for U_q(\hat{sl}_2) vertex models using an extended auxiliary space, deriving new T-Q relations and connecting to Baxter's operator in the 6-vertex model.

Contribution

It constructs a universal Q-operator with a four-parameter generalization, extending previous q-oscillator representations and deriving generalized T-Q relations.

Findings

Derived explicit Q-operator for the 6-vertex model

Established connection with Baxter's operator

Generalized T-Q relations with parameter shifts

Abstract

In this paper, we construct a Q-operator as a trace of a representation of the universal R-matrix of $U_q(\hat{sl}_2)$ 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.