  We continue the study of the gl(1|1) Wess-Zumino-Witten model. The
Knizhnik-Zamolodchikov equations for the one, two, three and four point
functions are analyzed, for vertex operators corresponding to typical and
projective representations. We illustrate their interplay with the logarithmic
global conformal Ward identities. We compute the four point function for one
projective and three typical representations. Three coupled first order
Knizhnik-Zamolodchikov equations are integrated consecutively in terms of
generalized hypergeometric functions, and we assemble the solutions into a
local correlator. Moreover, we prove crossing symmetry of the four point
function of four typical representations at generic momenta. Throughout, the
map between the gl(1|1) Wess-Zumino-Witten model and symplectic fermions is
exploited and extended.
