Restrictions of irreducible representations of algebraic groups of type $A_n$ in characteristic $0$ to subgroups of type $A_1\times A_1$

Restrictions of irreducible representations of algebraic groups of type $A_n$ in characteristic $0$ to naturally embedded subgroups of type $A_1\times A_1$ are studied. The composition factors of such restrictions are determined. For $n=3$ the multiplicities of these factors are found.