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Abstract

Let g be a 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 dimension of the corresponding highest weight modules.