  We calculate the eigenvalues of the next-to-leading kernel for the BFKL
equation in the adjoint representation of the gauge group $SU(N_c)$ in the N=4
supersymmetric Yang-Mills model. These eigenvalues are used to obtain the high
energy behavior of the remainder function for the 6-point scattering amplitude
with the maximal helicity violation in the kinematical regions containing the
Mandelstam cut contribution. The leading and next-to-leading singularities of
the corresponding collinear anomalous dimension are calculated in all orders of
perturbation theory. We compare our result with the known collinear limit and
with the recently suggested ansatz for the remainder function in three loops
and obtain the full agreement providing that the numerical parameters in this
anzatz are chosen in an appropriate way.

High Energy Physics - Theory;High Energy Physics - Phenomenology