The restrictions of representations of special linear groups to subsystem subgroups of type $A_1\times A_1$

The restrictions of irreducible representations of the special linear group over an algebraically closed field of positive characteristic $p$ to subsystem subgroups of type $A_1\times A_1$ are studied. The symmetry of the set of highest weights of composition factors is proven. The "big" composition factors of such restrictions for the arbitrary $p$-restricted representations are found. These results will be used for the complete description of such restrictions.