  We present a complete solution of the WZW model on the supergroup GL(1|1).
Our analysis begins with a careful study of its minisuperspace limit
(``harmonic analysis on the supergroup''). Its spectrum is shown to contain
indecomposable representations. This is interpreted as a geometric signal for
the appearance of logarithms in the correlators of the full field theory. We
then discuss the representation theory of the gl(1|1) current algebra and
propose an Ansatz for the state space of the WZW model. The latter is
established through an explicit computation of the correlation function. We
show in particular, that the 4-point functions of the theory factorize on the
proposed set of states and that the model possesses an interesting spectral
flow symmetry. The note concludes with some remarks on generalizations to other
supergroups.
