NULL-VECTORS IN INTEGRABLE FIELD-THEORY

The form factor bootstrap approach allows to construct the space of lo cal fields in the massive restricted sine-Gordon model. This space has to be isomorphic to that of the corresponding minimal model of confor mal field theory. We describe the subspaces which correspond to the Ve rma modules of primary fields in terms of the commutative algebra of l ocal integrals of motion and of a fermion (Neveu-Schwarz or Ramond dep ending on the particular primary held). The description of null-vector s relies on the relation between form factors and deformed hyper-ellip tic integrals. The null-vectors correspond to the deformed exact forms and to the deformed Riemann bilinear identity. In the operator langua ge, the null-vectors are created by the action of two operators Q (lin ear in the fermion) and C (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 Q a nd C we obtain a new, very compact, description of the KdV hierarchy. We also discuss a beautiful relation with the method of Whitman.