Mathematical Sciences: Representation Theory

数学科学：表示论

• 批准号: 8801579
• 负责人: Herve Jacquet
• 金额: $ 18.12万
• 依托单位: Columbia University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1988
• 资助国家: 美国
• 起止时间: 1988-07-01 至 1991-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8801579&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Representation; Theory

The research on this project will be carried out by two investigators, the principal investigator Herve Jacquet and his postdoctoral associate Michael Heumos. Jacquet will continue his efforts at generalizing his new trace formula. Results on special values of L-functions, the determination of the residual spectrum of the general linear group and a better understanding of the Weil representation are among the long range goals of the project. Heumos will study models for unitary representations of GLn over a p-adic field. These models generalize the standard Whittaker model and are subgroups of GLn. Examples suggest that perhaps all unitary representations embed uniquely in a unique model. This would provide a new perspective to the study of unitary representations of the p-adic GLn and would have widespread applications. This research is in the area of number theory commonly known as the "Langland's program". It applies advanced notions from many areas, most especially modern analysis, to answer fundamental questions in arithmetic.

该项目的研究将由两位研究人员进行，他们是首席研究员Herve Jacquet和他的博士后助理Michael Heumos。雅凯将继续努力推广他的新道式。关于l函数的特殊值的结果，一般线性群的残差谱的确定以及更好地理解Weil表示是该项目的长期目标之一。Heumos将研究p进域上GLn的酉表示模型。这些模型推广了标准惠特克模型，是GLn的子群。示例表明，也许所有的单一表示都唯一地嵌入到一个唯一的模型中。这将为研究p进GLn的酉表示提供一个新的视角，具有广泛的应用价值。这项研究是在数论领域，通常被称为“朗兰程序”。它应用了许多领域的先进概念，尤其是现代分析，来回答算术中的基本问题。