  We analyze a completely integrable two-dimensional quantum-mechanical model
that emerged in the recent studies of the compound gluonic states in
multi-color QCD at high energy. The model represents a generalization of the
well-known homogenous Heisenberg spin magnet to infinite-dimensional
representations of the SL(2,C) group and can be reformulated within the Quantum
Inverse Scattering Method. Solving the Yang-Baxter equation, we obtain the
R-matrix for the SL(2,C) representations of the principal series and discuss
its properties. We explicitly construct the Baxter Q-operator for this model
and show how it can be used to determine the energy spectrum. We apply
Sklyanin's method of the Separated Variables to obtain an integral
representation for the eigenfunctions of the Hamiltonian. We demonstrate that
the language of Feynman diagrams supplemented with the method of uniqueness
provide a powerful technique for analyzing the properties of the model.
