  It is well-known that solutions to the string equation are generated by
elements of Sato's Grassmannian which are invariant under action of some
differential operator. Here it is shown that this operator is nothing else than
the infinitesimal operator of the group of additional symmetries of the KdV
flow. This is done for KdV hierarchies of arbitrary orders. Virasoro
constraints are obtained in a slightly more general form than they are usually
written.
