  We study corrections due to two Pomeron exchanges to the inclusive 1-jet
production cross section in the Regge limit of perturbative QCD for a finite
number of colors. By considering deep inelastic scattering on a weakly bound
two-nucleon system, we carefully follow the logic of the AGK cutting rules and
show, for the single inclusive cross section, that, due to the reggeization of
the gluon, modifications of the AGK cutting rules appear. As our main result,
we investigate and calculate the jet production vertex in the presence of a
two-Pomeron cut correction. Compared to previous studies, we find a novel
structure of the jet vertex which has not been considered before. We discuss a
few implications of this new piece.
