Conformal blocks in the QCD Pomeron formalism

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