论文标题
通过bruhat-tits理论的参数化未经托里的共轭类别
Parameterizing Conjugacy Classes of Unramified Tori via Bruhat-Tits Theory
论文作者
论文摘要
假设$ k $是一个非架构的本地字段，$ k $是$ k $的最大不合格的扩展名，而$ \ mathbf {g} $是连接的还原$ k $ -group。在本文中，我们通过Bruhat-tits理论提供参数化：$ \ Mathbf {g} $的$ k $ -tori的理性共轭类，分裂在$ k $上； $ \ mathbf {g} $的未受到扭曲的Levi子组的$ K $ -SPLIT组件的理性和稳定共轭类；以及$ \ mathbf {g} $的未经扭曲的广义Levi子组的理性共轭类。我们还为有限的谎言类型组提供了类似对象的参数化。
Suppose $k$ is a nonarchimedean local field, $K$ is a maximally unramified extension of $k$, and $\mathbf{G}$ is a connected reductive $k$-group. In this paper we provide parameterizations via Bruhat-Tits theory of: the rational conjugacy classes of $k$-tori in $\mathbf{G}$ that split over $K$; the rational and stable conjugacy classes of the $K$-split components of the centers of unramified twisted Levi subgroups of $\mathbf{G}$; and the rational conjugacy classes of unramified twisted generalized Levi subgroups of $\mathbf{G}$. We also provide parameterizations of analogous objects for finite groups of Lie type.
