  Cylindrical gravitational waves are interesting because they enjoy an
infinite dimensional symmetry called Geroch symmetry. In this paper, we compute
the 2-particle tree-level S-matrix for cylindrical gravitational waves. The
model we use is a dimensional reduction of general relativity to two spacetime
dimensions. The reduced theory is a nonlinear sigma model. We discuss an SO(2)
symmetry of the amplitudes which is a special case of Geroch symmetry.
