Multiplicity-free representations of algebraic groups II

We continue our work (started in ``Multiplicity-free representations of algebraic groups", arXiv:2101.04476), on the program of classifying triples $(X,Y,V)$, where $X,Y$ are simple algebraic groups over an algebraically closed field of characteristic zero with $X<Y$, and $V$ is an irreducible module for $Y$ such that the restriction $V\downarrow X$ is multiplicity-free. In this paper we handle the case where $X$ is of type $A$, and is irreducibly embedded in $Y$ of type $B,C$ or $D$. It turns out that there are relatively few triples for $X$ of arbitrary rank, but a number of interesting exceptional examples arise for small ranks.