标题： 提升Deligne-Lusztig约化和几何Coxeter型元素 显示英文标题

标题： Lifting Deligne-Lusztig Reduction and Geometric Coxeter Type Elements

摘要： 在Rapoport-Zink空间的特殊纤维仅为经典Deligne-Lusztig流形的并集的Shimura流形情况下，被称为完全Hodge-Newton可分解的情况，在过去曾受到广泛关注。近年来，研究重点转向识别完全Hode-Newton可分解情况之外的易于处理的情况，并已确定了一些实例，其中仅出现经典Deligne-Lusztig流形与更简单空间的乘积。在我们的论文中，我们提供了一个统一的框架来捕捉这些现象。通过研究从仿射旗流形到环群的提升，并将其与Deligne-Lusztig约化方法相结合，我们的主要结果是一个强有力的准则，用以证明仿射Deligne-Lusztig流形是经典Deligne-Lusztig流形与仿射空间和带点仿射空间的乘积。我们引入了一类称为具有几何Coxeter类型的元素，其严格包含之前研究过的概念，如正Coxeter类型或有限Coxeter类型。这些具有几何Coxeter类型的元素满足我们主要结果的条件，以及Milićević-Viehmann引入的Newton分层条件。 显示英文摘要

摘要： Cases of Shimura varieties where the special fibre of a Rapoport-Zink space is simply the union of classical Deligne-Lusztig varieties are known as fully Hodge-Newton decomposable ones, and have been studied with great interest in the past. In recent times, the focus has shifted to identify tractable cases beyond the fully Hodge-Newton decomposable ones, and several instances have been identified where only products of classical Deligne-Lusztig varities with simpler spaces occur. In our paper, we provide a uniform framework to capture these phenomena. By studying liftings from the affine flag variety to the loop group and combining them with the Deligne-Lusztig reduction method, our main result is a powerful criterion to show that an affine Deligne-Lusztig variety is the product of a classical Deligne-Lusztig variety with affine spaces and pointed affine spaces. We introduce the class of elements that we call having geometric Coxeter type, strictly including previously studied notions such as positive Coxeter type or finite Coxeter type. These elements of geometric Coxeter type satisfy the conditions for our main result and also a condition on the Newton stratification introduced by Mili\'cevi\'c-Viehmann.