论文标题
某些球形商的参数化，结构和bruhat顺序
Parametrization, structure and Bruhat order of certain spherical quotients
论文作者
论文摘要
令$ g $为一个还原的代数群，让$ z $成为lie代数的nilpotent元素$ e $ $ g $的稳定器。我们考虑$ z $在$ g $的国旗品种上的操作，我们专注于此操作具有有限数量的轨道（即$ z $是球形子组）的情况。例如，如果$ e $具有高度$ 2 $，则可以。在这种情况下，我们给出了$ z $ -Orbits的参数化，我们表明每个$ z $ -Orbit都有一个代数仿射捆绑结构。特别是，在$ a $的类型中，我们推断每个轨道都有天然细胞分解。为了研究轨道的（强）Bruhat顺序，我们对与Coxeter系统相关的某些商定义了抽象的部分顺序。在类型$ a $中，我们表明可以以这种方式描述$ z $ - 孔的bruhat顺序。
Let $G$ be a reductive algebraic group and let $Z$ be the stabilizer of a nilpotent element $e$ of the Lie algebra of $G$. We consider the action of $Z$ on the flag variety of $G$, and we focus on the case where this action has a finite number of orbits (i.e., $Z$ is a spherical subgroup). This holds for instance if $e$ has height $2$. In this case we give a parametrization of the $Z$-orbits and we show that each $Z$-orbit has a structure of algebraic affine bundle. In particular, in type $A$, we deduce that each orbit has a natural cell decomposition. In the aim to study the (strong) Bruhat order of the orbits, we define an abstract partial order on certain quotients associated to a Coxeter system. In type $A$, we show that the Bruhat order of the $Z$-orbits can be described in this way.
