Quantum Group Representations and Baxter Equation

TL;DR

This paper introduces a universal algebraic method to derive fusion rules and Baxter equations for integrable models with quantum affine algebra symmetry, utilizing the universal R-matrix and q-oscillator representations.

Contribution

It presents a novel universal algebraic procedure for constructing Baxter Q-operators and fusion rules applicable to any model with $U_q( ilde{sl}_2)$ symmetry, expanding the theoretical framework.

Findings

Derived universal Baxter Q-operator from q-oscillator representations.

Established algebraic properties of the Q-operator.

Provided a universal method applicable to various integrable models.

Abstract

In this paper we propose algebraic universal procedure for deriving "fusion rules" and Baxter equation for any integrable model with $U_q(\widehat{sl}_2)$ symmetry of Quantum Inverse Scattering Method. Universal Baxter Q- operator is got from the certain infinite dimensional representation called q-oscillator one of the Universal R- matrix for $U_q(\widehat{sl}_2)$ affine algebra (first proposed by V. Bazhanov, S.Lukyanov and A.Zamolodchikov for quantum KdV case). We also examine the algebraic properties of Q-operator.