  We study the structure of superselection sectors of an arbitrary perturbation
of a conformal field theory. We describe how a restriction of the q-deformed
$\hat{sl(2)}$ affine Lie algebra symmetry of the sine-Gordon theory can be used
to derive the S-matrices of the $\Phi^{(1,3)}$ perturbations of the minimal
unitary series. This analysis provides an identification of fields which create
the massive kink spectrum. We investigate the ultraviolet limit of the
restricted sine-Gordon model, and explain the relation between the restriction
and the Fock space cohomology of minimal models. We also comment on the
structure of degenerate vacuum states. Deformed Serre relations are proven for
arbitrary affine Toda theories, and it is shown in certain cases how relations
of the Serre type become fractional spin supersymmetry relations upon
restriction.
