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 U-q(<(sl)over cap (2)>) 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 U-q(<(sl)over cap (2)>) 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.