Reducibility of Scalar Generalized Verma Modules of Minimal Parabolic Type

Let [Formula: see text] be a classical complex simple Lie algebra and [Formula: see text] be a parabolic subalgebra. A generalized Verma module [Formula: see text] is called a scalar generalized Verma module if it is induced from a one-dimensional representation of [Formula: see text]. In this paper, we 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.