  Three explicit and equivalent representations for the monodromy of the
conformal blocks in the SL(2,C)/SU(2) WZNW model are proposed in terms of the
same quantity computed in Liouville field theory. We show that there are two
possible fusion matrices in this model. This is due to the fact that the
conformal blocks, being solutions to the Knizhnik-Zamolodchikov equation, have
a singularity when the SL(2,C) isospin coordinate x equals the worldsheet
variable z. We study the asymptotic behaviour of the conformal block when x
goes to z. The obtained relation inserted into a four point correlation
function in the SL(2,C)/SU(2) WZNW model gives some expression in terms of two
correlation functions in Liouville field theory.
