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arXiv · 2306.01231

Reducibility of scalar generalized Verma modules of minimal parabolic type

Jing Jiang
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Abstract

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.

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Jing Jiang. 2023-06-02. Reducibility of scalar generalized Verma modules of minimal parabolic type. https://arxiv.org/abs/2306.01231

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