  The form factor bootstrap approach allows to construct the space of local
fields in the massive restricted sine-Gordon model. This space has to be
isomorphic to that of the corresponding minimal model of conformal field
theory. We describe the subspaces which correspond to the Verma modules of
primary fields in terms of the commutative algebra of local integrals of motion
and of a fermion (Neveu-Schwarz or Ramond depending on the particular primary
field). The description of null-vectors relies on the relation between form
factors and deformed hyper-elliptic integrals. The null-vectors correspond to
the deformed exact forms and to the deformed Riemann bilinear identity. In the
operator language, the null-vectors are created by the action of two operators
$\CQ$ (linear in the fermion) and $\CC$ (quadratic in the fermion). We show
that by factorizing out the null-vectors one gets the space of operators with
the correct character. In the classical limit, using the operators $\CQ$ and
$\CC$ we obtain a new, very compact, description of the KdV hierarchy. We also
discuss a beautiful relation with the method of Whitham.
