Reducibility of scalar generalized Verma modules of minimal parabolic type

2023/06/02 by Jiang, Jing
#FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2306.01231

Abstract

Let \mathfrakg be a classical complex simple Lie algebra and \mathfrakq 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 \mathfrakq. 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.

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