广义仿射建筑
Generalized affine buildings
摘要：
本文主要研究非离散仿射建筑物的几何性质。我们涵盖特别是仿射$Λ$ -建筑物，这是介绍了柯蒂斯贝内特在1990年，并已被证明是有用的应用程序。主要结果如下：首先证明了无穷远处建筑物生态同构的一个扩张定理。此外，补充一个联合项目与L。Kramer和R. Weiss，我们给出了一个代数证明的存在性（必然）非离散仿射建筑物有铃木-李建筑物在无穷远。大部分的努力是把推广的Kostant的凸性定理对称空间的设置单纯仿射和仿射$Λ$ -建筑物。证明是基于连接到表示论以及借用的方法从度量几何。
英文摘要：
In the present thesis geometric properties of non-discrete affine buildings are studied. We cover in particular affine $Λ$-buildings, which were introduced by Curtis Bennett in 1990 and which already have proven to be useful for applications. The main results are as follow: First we prove an extension theorem for ecological isomorphisms of buildings at infinity. Further, complementing a joint project with L. Kramer and R. Weiss, we give an algebraic proof of the existence of (necessarily) non-discrete affine buildings having Suzuki-Ree buildings at infinity. Most of the effort is put in the generalization of Kostant's convexity theorem for symmetric spaces in the setting of simplicial affine and affine $Λ$-buildings. The proofs are based on connections to representation theory as well as on methods borrowed from metric geometry.
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