  Let $\mathfrak{g}$ be a classical complex simple Lie algebra and
$\mathfrak{q}$ be a parabolic subalgebra. Generalized Verma module $M$ is
called a scalar generalized Verma module if it is induced from a
one-dimensional representation of $\mathfrak{q}$. In this paper, we will
determine the first diagonal-reducible point of scalar generalized Verma
modules associated to minimal parabolic subalgebras by computing explicitly the
Gelfand-Kirillov dimension of the corresponding highest weight modules.
