  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.
