  The conformal invariance properties of the QCD Pomeron in the transverse
plane allow us to give an explicit analytical expression for the conformal
eigenvectors in the mixed representation in terms of two conformal blocks, each
block being the product of an holomorphic times an antiholomorphic function.
This property is used to give an exact expression for various functions of
interest, the Pomeron amplitude in both momentum and impact-parameter
variables, the QCD dipole multiplicities and dipole-dipole cross-sections in
the whole parameter space, and we recover the expression of the four-point
gluon Green function given recently by Lipatov
