  In this paper we generalize the fermionic approach to the KP hierarchy
sudgested in the papers of Kyoto school 1981-1984 (Sato,Jimbo, Miwa...). The
main idea is that the components of the intertwiningoperators are in some sense
a generalization of free fermions for $gl_{\infty}$. We formulate in terms of
intertwining operators the integrable hierarchies related to Kac-Moody Lie
algebra symmetries. We write down explicitly the bosonization of these
operators for different choices of Heisenberg subalgebras. These different
realizations lead to different hierarchies of soliton equations. For example,
for $sl_N$-symmetries we get hierarchies obtained as $(n_1,..., n_s)$-reduction
from $s$-component KP $(n_1+...+n_s = N)$ introduced by V.Kac and J.Van de
Leur.

High Energy Physics - Theory