Representations of p-adic Groups

p进群的表示

• 批准号: 0100678
• 负责人: Jiu-Kang Yu
• 金额: $ 7.02万
• 依托单位: University of Maryland, College Park
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2001
• 资助国家: 美国
• 起止时间: 2001-07-01 至 2004-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0100678&HistoricalAwards=false
• 关键词: Representations; adic; Groups

The principal investigator pursues the representation theory of p-adic groups, centered on the structural theory of the p-adic groups via Bruhat-Tits theory, and the method of restriction on compact open subgroups. Specifically, combining his work on the construction of supercuspidal representations, explicit computations of Bruhat-Tits buildings and refined minimal K-types, the investigator studies refined types, Hecke algebra isomorphisms, and other related topics.The representation theory of p-adic groups, being an amazing theory in its own right, plays a prominent role in number theory and automorphic forms, hence is fundamental to applications of number theory to computing and cryptography. Recently there have been exciting new advances, including the investigator's construction of supercuspidal representations, which was considered most unreachable objects. These advances open up new questions, which is to be pursued in this project.

主要研究者追求p-adic群的表示理论，以通过Bruhat-Tits理论的p-adic群的结构理论和紧开子群的限制方法为中心。 具体来说，结合他的工作建设的supercuspidal表示，明确计算的Bruhat-Tits建筑物和精致的最小K型，研究者研究精致的类型，Hecke代数同构，和其他相关主题。表示理论的p-adic群，是一个惊人的理论本身，发挥了突出的作用，在数论和自守形式，因此是数论在计算和密码学中应用的基础。 最近有令人兴奋的新进展，包括研究人员的建设supercuspidal表示，这被认为是最遥不可及的对象。 这些进展提出了新的问题，本项目将继续探讨这些问题。