Representation Theory and Automorphic Forms

表示论和自守形式

• 批准号: 9970689
• 负责人: Gordan Savin
• 金额: $ 12.49万
• 依托单位: University of Utah
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1999
• 资助国家: 美国
• 起止时间: 1999-07-15 至 2002-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9970689&HistoricalAwards=false
• 关键词: Representation; Theory; Automorphic; Forms

AbstractSavinThis award supports research in several areas of representation theory and modular forms with applications to number theory. In particular, we propose to determine the Howe correspondence for generic square-integrable representations of classical p-adic groups. This work is based on the recent classification of generic square-integrable representations of classical p-adic groups due to Goran Muic. The theory of modular forms was born more then a century ago, as powerful techniques of complex analysis were introduced to attack classical problems in number theory. It has remained a vibrant mathematical subject throughout the 20th century with applications in physics, and more recently in computer science, coding theory in particular.

摘要萨文该奖项支持表示论和模形式及其在数论中的应用的多个领域的研究。特别是，我们建议确定经典 p 进群的通用平方可积表示的豪对应关系。 这项工作基于 Goran Muic 对经典 p-adic 群的通用平方可积表示的最新分类。模形式理论诞生于一个多世纪前，当时强大的复分析技术被引入来解决数论中的经典问题。在整个 20 世纪，它一直是一门充满活力的数学学科，在物理学中得到了应用，最近在计算机科学，特别是编码理论中得到了应用。