论文标题
Aggine Deligne- lusztig品种有限的Coxeter零件
Affine Deligne--Lusztig varieties with finite Coxeter parts
论文作者
论文摘要
在本文中，我们研究Aggine deligne--lusztig品种$ x_w（b）$当iWahori中的元素$ w $的有限部分 - weyl组是部分$σ$ -coxeter元素。我们证明，这样的$ W $是一个亲切的元素，$ x_w（b）\ neq \ emptyset $，仅当$ b $满足某个hodge - newton newton in newton in newdecomposanity条件。本文的主要结果是，对于这样的$ W $和$ b $，$ x_w（b）$具有简单的几何结构：$ b $的$σ$中性化合物在$ x_w（b）$的不可减至的成分上进行过渡性。每个不可减至的组件都是经典deligne- lusztig种类的迭代振动，而迭代的纤维是$ \ mathbb a^1 $或$ \ mathbb g_m $。
In this paper, we study affine Deligne--Lusztig varieties $X_w(b)$ when the finite part of the element $w$ in the Iwahori--Weyl group is a partial $σ$-Coxeter element. We show that such $w$ is a cordial element and $X_w(b) \neq \emptyset$ if and only if $b$ satisfies a certain Hodge--Newton indecomposability condition. The main result of this paper is that for such $w$ and $b$, $X_w(b)$ has a simple geometric structure: the $σ$-centralizer of $b$ acts transitively on the set of irreducible components of $X_w(b)$; and each irreducible component is an iterated fibration over a classical Deligne--Lusztig variety of Coxeter type, and the iterated fibers are either $\mathbb A^1$ or $\mathbb G_m$.
