论文标题
代数组和$ g $ - 完整的降低性：几何方法
Algebraic groups and $G$-complete reducibility: a geometric approach
论文作者
论文摘要
\ emph {$ g $ - 综合}亚组的概念在对代数组及其亚组结构的研究中很重要。它概括了从表示理论中完全降低的通常的想法：一般线性组的子组$ h $ $ g = {\ rm gl} _n（k）$ as $ g $ - completcomplets spleplectiple spleplectibles and Ploss Ploss Ploss Ploss Ploss仅当包含地图$ i \ colon h \ colon H \ colon h \ rightarrow {\ rightarrow {\ rimm gl} _n（k）$是$ s $ s $ IS $ IS $ IS $ HE。在这些注释中，我介绍了完全降低性及其应用理论，并使用几何不变理论解释了对主题的方法。
The notion of a \emph{$G$-completely reducible} subgroup is important in the study of algebraic groups and their subgroup structure. It generalizes the usual idea of complete reducibility from representation theory: a subgroup $H$ of a general linear group $G= {\rm GL}_n(k)$ is $G$-completely reducible if and only if the inclusion map $i\colon H\rightarrow {\rm GL}_n(k)$ is a completely reducible representation of $H$. In these notes I give an introduction to the theory of complete reducibility and its applications, and explain an approach to the subject using geometric invariant theory.
