论文标题
在$ sl的相对的霍斯基亚组中生成的离散子组（3，\ m athbb {c}）$ hee oh oh oh oh
Discrete subgroups generated by lattices in opposite horospherical subgroups of $SL(3,\mathbb{C})$ following Hee Oh
论文作者
论文摘要
我们证明，在$ sl（3，\ mathbb {c}）$的相对最小霍斯基亚组中生成的两个晶格产生的离散子组是算术的，因此由borel和borel和harish-chandra也是晶格。我们遵循OH在\ cite {ref13}中使用的方法和想法。在那里，哦，在最小的horosphical子组（n，\ mathbb {r}）$中的晶格证明了相同的结果。该方法包括研究相应的Levi子组的交通量的共轭作用，以获取$ sl（3，\ Mathbb {C}）$的合理结构，以研究霍斯基亚组中生成晶格的轨道。 Ratner的定理减少了闭合轨道的可能性。然后，通过生成的亚组的离散性，可以显示轨道的亲密性。最后，使用此信息，可以找到一种有理形式，以使晶格生成的子组算术。
We prove that a discrete subgroup generated by two lattices in opposite minimal horospherical subgroups of $SL(3,\mathbb{C})$ is arithmetic and thus by a Borel and Harish-Chandra also a lattice. We follow the method and ideas used by Oh in \cite{Ref13}. There, Oh proves the same result for lattices in minimal horospherical subgroups of $SL(n,\mathbb{R})$. The method consists of studying the orbits of the generating lattices in the horospherical subgroups under the conjugation action of the commutator of the corresponding Levi subgroup in order to obtain a rational structure for $SL(3,\mathbb{C})$. A theorem of Ratner reduces the possibilities for the closure of the orbits. Then, by the discreteness of the generated subgroup, it can be shown the closeness of the orbits. Finally, using this information, it's possible to find a rational form such that the subgroup generated by the lattices is arithmetic.
