Abstract In this article, we give a generalization of O’Halloran’s theorem that gives rise to families of Weyl modules with simple radicals. This generalization is then applied to simply connected, semisimple algebraic groups of types B, C, and D. We also construct families of Weyl modules with formal characters of length 4, and compute the extensions and cohomology of simple modules associated with these Weyl modules.

中文翻译：

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代数群的一些外尔模和上同调

摘要 在本文中，我们给出了 O'Halloran 定理的推广，该定理产生了具有简单根的 Weyl 模族。然后将这种概括应用于 B、C 和 D 类型的简单连接的半单代数群。我们还构造了长度为 4 的形式特征的 Weyl 模族，并计算与这些 Weyl 模相关的简单模的扩展和上同调。