Multi-color QCD at High Energies and Exactly Solvable Lattice Theories

We examine the generalized leading-logarithmic approximation (LLA) equations for compound states of n-reggeized gluons. It is shown that in multi-color QCD, when $N_c \rightarrow \infty$, these equations have a sufficient number of conservation laws to be exactly solvable. Holomorphic factorization of the wave functions is used to reduce the corresponding quantum mechanical problem to the solution of the one-dimensional Heisenberg model with the spins being the generators of the M$\ddot{o}$bius group of conformal transformations.