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

这一为期三年的奖项支持合作 算子K理论的研究， Paul之间的p-adic群的表示 鲍姆和奈杰尔希格森，宾夕法尼亚州 大学的罗杰·普利门 英国曼彻斯特大学。 本项目的目标是确定 Baum-Connes猜想的有效性 使用半单的情况，p-adic代数 组 调查人员还将探索 猜想与指数理论的关系 欧几里得建筑和库茨科建筑 半单群的猜想 拟议的研究将推动我们的 C ~* 代数的K-理论的理解 与p-adic组相关。 通过使 都是数论的结果 分析、拓扑和群表示 理论，K理论提供了一个适当的框架 用于表达和统一这些结果 领域的 该项目将受益于结合 Baum和Higson的几何观点， K理论和指数理论的经验， Plymen关于表象理论的工作， 代数（p-adic）群

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.