  The Conformal Field Theory of the current algebra of the centrally extended
2-d Euclidean group is analyzed. Its representations can be written in terms of
four free fields (without background charge) with signature ($-$+++). We
construct all irreducible representations of the current algebra with unitary
base out of the free fields and their orbifolds. This is used to investigate
the spectrum and scattering of strings moving in the background of a
gravitational wave. We find that all the dynamics happens in the transverse
space or the longitunal one but not both.
