U.S.-U.K. Cooperative Research: Operator K-Theory and Representation Theory for Semisimple p-adic Groups

这个为期三年的奖项支持宾夕法尼亚州立大学的Paul Baum和Nigel Higson以及英国曼彻斯特大学的Roger Plymen在算子k理论和p进群表示方面的合作研究。这个项目的目的是确定的有效性Baum-Connes猜想使用半简单，p进代数群的情况下。研究人员还将探索该猜想与欧几里得建筑的指数理论和半简单p进群的库茨科猜想的关系。提出的研究将促进我们对与p进群相关的C*代数的k理论的理解。通过汇集数论、分析、拓扑学和群表示理论的结果，k理论为表达和统一这些领域的结果提供了一个适当的框架。这个项目将受益于结合Baum和Higson在k理论和指标理论上的几何观点和经验，以及Plymen在表征理论和代数（p-adic）群上的工作。

This three-year award supports cooperative research in operator K-theory and representation of p-adic groups between Paul Baum and Nigel Higson, Pennsylvania State University, and Roger Plymen from the University of Manchester in the United Kingdom. The objective of this project is to determine the validity of the Baum-Connes conjecture using the case of semi-simple, p-adic algebraic groups. The investigators will also explore the conjecture's relationship to index theory for Euclidean buildings and to Kutsko's conjecture for semi-simple, p-adic groups. The proposed research will advance our understanding of the K-theory of C* algebras associated with p-adic groups. By bringing together results from the number theory, analysis, topology and group representation theory, K-theory provides an adequate framework for expressing and unifying results in these fields. This project will benefit by combining Baum and Higson's geometric viewpoint and experience on K-theory and index theory with Plymen's work on representational theory and algebraic (p-adic) groups.