论文标题
仿期建筑物中的烟囱缩回仿射旗品种中的编码轨道
Chimney retractions in affine buildings encode orbits in affine flag varieties
论文作者
论文摘要
本文确定了缩回的几何形状与任意仿射建筑物的折叠画廊的组合之间的关系，因此提供了一个统一的框架来研究仿射标志品种中的轨道。我们介绍了任何X型建筑物X的标记折叠画廊的概念，并使用它们来描述烟囱缩回的预示。当X是具有仿射山雀系统的小组的建筑物时，例如在本地字段上为集团的Bruhat-tits建筑物建筑物时，我们可以将标记的折叠画廊和阴影联系起来，以在Aggine Flag品种中的双固定相交。该结果概括了作者先前与NAQVI在函数字段上的联合工作。
This paper determines the relationship between the geometry of retractions and the combinatorics of folded galleries for arbitrary affine buildings, and so provides a unified framework to study orbits in affine flag varieties. We introduce the notion of labeled folded galleries for any affine building X and use these to describe the preimages of chimney retractions. When X is the building for a group with an affine Tits system, such as the Bruhat-Tits building for a group over a local field, we can then relate labeled folded galleries and shadows to double coset intersections in affine flag varieties. This result generalizes the authors' previous joint work with Naqvi on groups over function fields.
