  We study the algebraic formulation of exact factorizable S-matrices for
integrable two-dimensional field theories. We show that different formulations
of the S-matrices for the Potts field theory are essentially equivalent, in the
sense that they can be expressed in the same way as elements of the
Temperley-Lieb algebra, in various representations. This enables us to
construct the S-matrices for certain nonlinear sigma models that are invariant
under the Lie ``supersymmetry'' algebras sl(m+n|n) (m=1,2; n>0), both for the
bulk and for the boundary, simply by using another representation of the same
algebra. These S-matrices represent the perturbation of the conformal theory at
theta=pi by a small change in the topological angle theta. The m=1, n=1 theory
has applications to the spin quantum Hall transition in disordered fermion
systems. We also find S-matrices describing the flow from weak to strong
coupling, both for theta=0 and theta=pi, in certain other supersymmetric sigma
models.
