Representations of the LL BFKL kernel and the bootstrap

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 Mobius 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. (author)