在阿贝尔幂零根基上自由的\(\mathfrak{so}_n(\mathbb{C})\) - 模
$\mathfrak{so}_n(\mathbb{C})$-modules which are free over an abelian nilradical
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中文总结 AI 辅助
研究对限制到极大抛物子代数阿贝尔幂零根基泛包络代数上秩为\(1\)自由的\(\mathfrak{so}_n(\mathbb{C})\) - 模范畴进行分类，通过证明其一般性及给出非单情形描述，体现权模与非权模联系。
中文摘要 AI 辅助
本文对\(\mathfrak{so}_n(\mathbb{C})\) - 模的范畴进行分类，这些模限制到极大抛物子代数的阿贝尔幂零根基的泛包络代数上时秩为\(1\)自由。证明它们一般是单的，给出非单情形下子模的明确描述。该范畴体现了权模与非权模之间的某种联系。
英文摘要
In this paper, we classify the category of $\mathfrak{so}_n(\mathbb{C})$-modules whose restrictions to the universal enveloping algebra of the abelian nilradical of a maximal parabolic subalgebra are free of rank $1$. We show that they generically are simple, and give an explicit description of submodules in the non-simple case. This category embodies a certain connection between weight modules and non-weight modules.
