On the restrictions of modular representations of the group $SL_{n+1}(K)$ to subgroups $SL_{r+1}(K)$ with $r<n$

Restrictions of irreducible $p$-restricted representations of the algebraic group $SL_{n+1}(K)$ to naturally embedded subgroups $SL_{r+1}(K)$ with $r<n$ are studied. Let $n>2$ and $\omega=\sum_{i=1}^nm_i\omega_i$ be the highest weight of a representation considered. The composition factors of such restrictions are determined in the case where $r=2$ and $m_i+m_{i+1}+m_{i+2}+2<p$ for all $i<n-1$. For restrictions of arbitrary representations some classes of big composition factors are found as well.