  Different forms of the BFKL kernel both in coordinate and momentum
representations may appear as a result of different gauge choices and/or inner
scalar products of the color singlet states. We study a spectral representation
of the BFKL kernel not defined on the Moebius space of functions but on a
deformation of it, which provides the usual bootstrap property due to gluon
reggeization. In this space the corresponding symmetry is made explicit
introducing a deformed realization of the sl(2,C) algebra.
