Root groups in totally disconnected locally compact groups

这项提议的总主题涉及完全不相连的、局部紧凑的(TDLC)组和作用于建筑物的组。在过去的二十年里，TDLC小组一直是一个非常活跃的研究主题。局部有限建筑物的自同构群构成了这类群的一个重要的例子。RGD系统是建筑的群论方法，每个RGD系统都配备了一个根系和一族根群。George Willis教授在一般的TDLC群中引入了根和根群的概念，它可以看作是一种特殊(即球形)RGD-系统的根系和根群的类似物。在这个项目中，我们将研究一般RGD-系统的根和根群这两个概念之间的联系，并试图找出RGD-系统中根群的性质在多大程度上推广到任意TDLC群中的根群。

The general theme of this proposal concerns totally disconnected, locally compact (tdlc) groups and groups acting on buildings. Over the last two decades tdlc groups have been a very active topic of research. Groups of automorphisms of locally finite buildings form an important family of examples of such groups. RGD-systems are the group theoretical approach to buildings and every RGD-system comes equipped with a root system and a family of root groups. Prof. George Willis introduced a notion of roots and root groups in general tdlc groups, which can be seen as analogues of the root system and the root groups of RGD-systems of a special (i.e. spherical) type. In this project we will investigate the connection between the two notions of roots and root groups of general RGD-systems and we will try to find out to what extent properties of the root groups in RGD-systems generalize to the root groups in arbitrary tdlc groups.