  The paper math.AG/0108100 gives a construction of the total descendent
potential corresponding to a semisimple Frobenius manifold. In math.AG/0209205,
it is proved that the total descendent potential corresponding to K. Saito's
Frobenius structure on the parameter space of the miniversal deformation of the
A_{n-1}-singularity satisfies the modulo-n reduction of the KP-hierarchy. In
this paper, we identify the hierarchy satisfied by the total descendent
potential of a simple singularity of the A,D,E-type. Our description of the
hierarchy is parallel to the vertex operator construction of Kac -- Wakimoto
except that we give both some general integral formulas and explicit numerical
values for certain coefficients which in the Kac -- Wakimoto theory are studied
on a case-by-case basis and remain, generally speaking, unknown.
