论文标题
还原性群体对同质空间的无效行动
Nondivergence of Reductive group action on Homogeneous Spaces
论文作者
论文摘要
让$ g/γ$成为其算术晶格的半圣谎言组$ g $的商。令$ h $为$ g $的还原代数子组，以$ g/γ$作用。我们感兴趣的问题是，是否有一组紧凑的$ g/γ$与每个H轨道相交。我们表明，这可以通过单个代数原因来解释这一问题，该原因将以前的几个结果推广到了这个问题。 实际上，获得了一个更一般的结果：当$ h $是一个$ g $的封闭子组时，满足$ h = am $的$ m $ a $ semisimple，以及$ a $ a $ a $ a $ \ a $ \ a $ \ mathbb {r} $ - 对角线瓦尼兹布式的亚组包含在$ g $中的$ m $ g $中的$ h $ h $ h $ h $ h $ h $ h $ h $ h $ h $ h $ h $ h $ h $ h $ h $ h的失败，则是a $ m $的限制。代数障碍。
Let $G/Γ$ be the quotient of a semisimple Lie group $G$ by its arithmetic lattice. Let $H$ be a reductive algebraic subgroup of $G$ acting on $G/Γ$. The question we are interested in is whether there is a compact set of $G/Γ$ that intersects every H-orbit. We show that the failure of this can be explained by a single algebraic reason, which generalizes several previous results towards this question. Indeed, a more general result was obtained: when $H$ is a closed subgroup of $G$ satisfying $H=AM$ with $M$ semisimple, and $A$ an $\mathbb{R}$-diagonalizable subgroup contained in the centralizer of $M$ in $G$, then the failure of every $H$-orbit intersecting nontrivially with a fixed compact set is caused by finitely many algebraic obstructions.
