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

美英合作研究：半单p进群的算子K理论和表示论

• 批准号: 9113392
• 负责人: Paul Baum
• 金额: $ 1.52万
• 依托单位: Pennsylvania State Univ University Park
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1992
• 资助国家: 美国
• 起止时间: 1992-03-15 至 1996-02-29
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9113392&HistoricalAwards=false
• 关键词: U.S.; U.K.; Cooperative; Research; Operator

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.

这项为期三年的奖项支持宾夕法尼亚州立大学保罗·鲍姆和奈杰尔·希格森在算子K理论和p-ady群表示方面的合作研究，以及来自英国曼彻斯特大学的罗杰·普莱门。本项目的目的是利用半单p-进代数群的情况来确定Baum-Connes猜想的有效性。研究人员还将探索该猜想与欧几里得建筑的指数理论以及半单p-进群的Kutsko猜想之间的关系。这一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。通过结合数论、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足够的框架。这个项目将把Baum和Higson在K理论和指数理论方面的几何观点和经验与Plymen在表象理论和代数(p-adi)群方面的工作结合起来。