Mathematical Sciences: Arithmetic Groups, P-adic Groups and Representation Theory

本课题主要研究p-add群表示理论中的两个相关问题。一个问题是在局部域上的约化群的可容许表示中寻找某些紧开子群的不变量。另一个是关于代数Q-群的Steinberg模与其算术子群的上同调之间的关系。本研究是关于p-进群的表示理论的研究。首席研究员将试图找到衡量这些群的某些性质的不变量。这项工作将对自同构形的理论产生重要的影响。代数学家和数学家都会对它感兴趣。

This project is concerned with two related problems in the representation theory of p-adic groups. One is concerned with finding invariants of certain compact open subgroups in admissible representations of reductive groups over local fields. The other is concerned with the relationship between the Steinberg module of an algebraic Q-group, and the cohomology of its arithmetic subgroups. This research is in the area of representation theory of p-adic groups. The principal investigator will try to find invariants which measure certain properties of these groups. This work would have important implications for the theory of automorphic forms. It will be of interest to algebraists and number theorists alike.