  Starting from a given S-matrix of an integrable quantum field theory in $1+1$
dimensions, and knowledge of its on-shell quantum group symmetries, we describe
how to extend the symmetry to the space of fields. This is accomplished by
introducing an adjoint action of the symmetry generators on fields, and
specifying the form factors of descendents. The braiding relations of quantum
field multiplets is shown to be given by the universal $\CR$-matrix. We develop
in some detail the case of infinite dimensional Yangian symmetry. We show that
the quantum double of the Yangian is a Hopf algebra deformation of a level zero
Kac-Moody algebra that preserves its finite dimensional Lie subalgebra. The
fields form infinite dimensional Verma-module representations; in particular
the energy-momentum tensor and isotopic current are in the same multiplet.
