\phi_l (y | \alpha_s).
\nonumber\end{aligned}$$ Taking the known LO contribution on the right hand side yields a differential equation which has the solution: $$\begin{aligned}
\label{eigfunc-beta}
\phi_j(x | \alpha_s)
\sim
\left[ x \bar x \right]^{\frac{3}{2} - \frac{\beta}{g}}
C_j^{\frac{3}{2}-\frac{\beta}{g}}( 2 x - 1 ).\end{aligned}$$ This result coincide in the large $N_f$ limit with the resummation of the vacuum polarization bubbles in Refs. [@Mik97; @GosKiv97] and verifies the ‘naive non-abelianization’ hypothesis employed there [@GosKiv97]. Moreover, it is very interesting to see that this hypothesis can be extended in our case to the [*whole*]{} $\beta$-function. Unfortunately, the eigenfunctions (\[eigfunc-beta\]) have no practical importance for the solution of the evolution equation. Obviously, in this treatment the special anomaly matrix contribution is completely discarded, however, it was demonstrated by numerical studies in Ref. [@Mue95] that a considerable cancellation occurs between the former and the symmetry breaking term due to the $\beta$-function for the real case $N_f=3$.

Summary.
========

In the present study we employ the powerful restrictions from the conformal algebra on the amplitudes in the massless theory. In the leading order of perturbation theory it enables us to give the solution of the evolution equations for the off-forward distribution functions in terms of the conformal 