Reducibility of scalar generalized Verma modules of minimal parabolic type II

Abstract

Let 𝔤 be an exceptional complex simple Lie algebra and 𝔮 be a parabolic subalgebra. A generalized Verma module M is called a scalar generalized Verma module if it is induced from a one-dimensional representation of 𝔮 . In this paper, we will determine the first diagonal-reducible point of scalar generalized Verma modules associated to minimal parabolic subalgebras of exceptional Lie algebras by computing explicitly the Gelfand–Kirillov (GK) dimension of the corresponding highest weight modules.