  We give branching formulas from $so(7,\mathbb{C})$ to $\mathfrak{g}_2$ for
generalized Verma modules attached to $\mathfrak{g}_2$-compatible parabolic
subalgebras of $so(7,\mathbb{C})$, and branching formulas from $\mathfrak{g}_2$
to $sl(3,\mathbb{C})$ for generalized Verma modules attached to
$sl(3,\mathbb{C})$-compatible parabolic subalgebras of $\mathfrak{g}_2$
respectively, under some assumptions on the parameters of generalized Verma
modules.
