  We represent a classical Maxwell-Bloch equation and related to it positive
part of the AKNS hierarchy in geometrical terms. The Maxwell-Bloch evolution is
given by an infinitesimal action of a nilpotent subalgebra $n_+$ of affine Lie
algebra $\hat {sl}_2$ on a Maxwell-Bloch phase space treated as a homogeneous
space of $n_+$. A space of local integrals of motion is described using
cohomology methods. We show that hamiltonian flows associated to the
Maxwell-Bloch local integrals of motion (i.e. positive AKNS flows) are
identified with an infinitesimal action of an abelian subalgebra of the
nilpotent subalgebra $n_+$ on a Maxwell- Bloch phase space. Possibilities of
quantization and latticization of Maxwell-Bloch equation are discussed.

High Energy Physics - Theory