Abstract In this article, we give some practical criteria to determine the reducibility of generalized Verma modules (induced from finite-dimensional modules) in the Hermitian symmetric case. Our criteria are given by the information of the corresponding highest weights of the finite-dimensional modules and relatively easy to verify. This article is inspired by earlier work of Kubo about Jantzen's criterion.

中文翻译：

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Hermitian 对称对的广义 Verma 模的可约性

摘要 在本文中，我们给出了一些实用标准来确定 Hermitian 对称情况下广义 Verma 模（从有限维模导出）的可约性。我们的标准是由有限维模块的相应最高权重的信息给出的，并且相对容易验证。这篇文章的灵感来自 Kubo 早期关于 Jantzen 标准的工作。