论文标题
Jantzen系数和广义Verma模块的简单性
Jantzen coefficients and simplicity of generalized Verma modules
论文作者
论文摘要
本文的主要目的是在研究$ \ mathcal {o}^\ mathfrak {p} $的研究中建立新工具。我们介绍了广义Verma模块的Jantzen系数。它来自Jantzen对广义Verma模块的简单标准，与$ \ Mathcal {O}^\ Mathfrak {p} $的结构有着深厚的关系。我们开发了一个减少过程来计算这些系数。为此，我们需要考虑具有最大非平凡奇异性的最大抛物线亚代代代代代代代代代代代代代代寄方剂的广义Verma模块，所谓的基本通用Verma模块。在本文中获得了此类模块的分类。作为我们结果的第一个应用，我们对Jantzen的简单标准进行了改进。
The main purpose of the paper is to establish new tools in the study of $\mathcal{O}^\mathfrak{p}$. We introduce the Jantzen coefficients of generalized Verma modules. It comes from the Jantzen's simplicity criteria for generalized Verma modules and has a deep relation with the structure of $\mathcal{O}^\mathfrak{p}$. We develop a reduction process to compute those coefficients. For which we need to consider generalized Verma modules induced from maximal parabolic subalgebras having maximal nontrivial singularity, so called basic generalized Verma modules. The classification of such modules is obtained in this paper. As the first application of our results, we give a refinement of Jantzen's simplicity criteria.
