Representations and Types of p-adic Groups

p进群的表示和类型

• 批准号: 0703258
• 负责人: Jiu-Kang Yu
• 金额: $ 14.98万
• 依托单位: Purdue University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2007
• 资助国家: 美国
• 起止时间: 2007-07-01 至 2011-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0703258&HistoricalAwards=false
• 关键词: Representations; Types; adic; Groups

Recent work of the PI and J. Kim provides enough types to classify all representations of many p-adic reductive groups. It remains to clarify what parametrizes those types. Moreover, the PI would like to understand how types are related to Langlands parameters. In addition, the project seek to study a problem related to Bruhat decomposition which arises in the theory of partial Bessel functions and local coefficients.These problems are all part of the Langlands program, one of the most influence programme in mathematics linking number theory and analysis. The representation theory problems here deal with some of the local analysis in the program, and have deep connections with arithmetic and geometry.

PI 和 J. Kim 最近的工作提供了足够的类型来对许多 p 进还原群的所有表示进行分类。 仍有待澄清这些类型的参数化内容。 此外，PI 希望了解类型与 Langlands 参数之间的关系。 此外，该项目还试图研究偏贝塞尔函数和局部系数理论中出现的与布鲁哈特分解相关的问题。这些问题都是朗兰兹纲领的一部分，朗兰兹纲领是连接数论和分析的数学中最具影响力的纲领之一。这里的表示论问题涉及程序中的一些局部分析，与算术和几何有很深的联系。