论文标题
将结构减少到抛物线亚组
Reduction of Structure to Parabolic Subgroups
论文作者
论文摘要
让$ g $成为一个特征领域而不是两个领域的仿射组。如果$ g $ -TORSOR被称为各向同性，如果将结构减少到适当的抛物线亚组为$ g $。该定义概括了仿射组的各向同性和中央简单代数的参与。 $ g $什么时候接纳各向异性扭转？在J. Tits的工作的基础上，我们为简单的小组回答了这个问题。在其根部系统的某些限制下，我们还为连接和半圣经$ g $提供答案。
Let $G$ be an affine group over a field of characteristic not two. A $G$-torsor is called isotropic if it admits reduction of structure to a proper parabolic subgroup of $G$. This definition generalizes isotropy of affine groups and involutions of central simple algebras. When does $G$ admit anisotropic torsors? Building on work of J. Tits, we answer this question for simple groups. We also give an answer for connected and semisimple $G$ under certain restrictions on its root system.
