The Congruence Subgroup Problem and Groups of Finite Representation Type

9700474 Rapinchuk这个奖项为数域上S--线性代数群的算术子群的同余子群问题的继续提供资金。主要的研究人员将尝试使用不同的有界性条件(有界生成和相似性质)、表示理论的方法(Kazhdan的性质(T))等多种技巧来证明一些新的群的同余核的中心性，他还将研究具有有限表示类型的群的性质和一些有限生成群的表示变体。这项研究属于数论的一般数学领域。数论的历史根源在于对整数的研究，它解决了一些问题，比如一个整数被另一个整数整除的问题。它是数学中最古老的分支之一，出于纯粹的美学原因，人们追寻了许多个世纪。然而，在过去的半个世纪里，它已经成为数据传输和处理以及通信系统等领域的各种应用中不可或缺的工具。

9700474 Rapinchuk This award provides funding for a continuing of the congruence subgroup problem for S-arithmetic subgroups of linear algebraic groups over number fields. The principal investigator will attempt to prove the centrality of the congruence kernel for some new classes of groups using a variety of techniques such as different boundedness conditions (bounded generation and similar properties), methods of representation theory (property (T) of Kazhdan), etc. He will also study the properties of groups having finite representation type and the representation varieties of some finitely generated groups. This research falls into the general mathematical field of Number Theory. Number Theory has its historical roots in the study of the whole numbers, addressing such questions as those dealing with the divisibility of one whole number by another. It is among the oldest branches of mathematics and was pursued for many centuries for purely aesthetic reasons. However, within the last half century it has become an indispensable tool in diverse applications in areas such as data transmission and processing, and communication systems.