Quantum group representations and the Baxter equation

In this article we propose an algebraic universal procedure for deriving the “fusion rules” and the Baxter equation for any integrable model with Uq(sl2) symmetry by means of the quantum inverse scattering method. The universal Baxter Q-operator is obtained from a certain infinite dimensional representation called q-oscillator representation of the universal R-matrix for the Uq(sl2) affine algebra (first proposed by V. Bazhanov, S. Lukyanov and A. Zamolodchikov [hep-th/9604044] for the quantum KdV case). We also examine the algebraic properties of the Q-operator.