Topological Methods in Representation Theory and Automorphic Forms

表示论和自守形式中的拓扑方法

• 批准号: 9803862
• 负责人: Kari Vilonen
• 金额: $ 8.84万
• 依托单位: Brandeis University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1998
• 资助国家: 美国
• 起止时间: 1998-08-01 至 2001-01-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9803862&HistoricalAwards=false
• 关键词: Topological; Methods; Representation; Theory; Automorphic

9803862 Vilonen This research program consists of three separate, but intimately related, projects. The first one, joint with Wilfried Schmid, concerns one of the important remaining questions in representation theory of reductive Lie groups: determining all of their unitary representations. They will attack this problem using the geometric techniques they developed to prove the Barbasch-Vogan conjecture. The second project, joint with E.Frenkel, D.Gaitsgory, and D.Kazhdan, deals with the Langlands conjectures. They will continue their work on the geometric Langlands conjecture and the geometric theory of Whittaker functions. The purpose of the third project, joint with Mirkovic, is to develop geometric techniques for representation theory of algebraic groups. This project has also turned out to be important for work on the geometric Langlands conjecture. The goal is to apply their methods to representation theory of algebraic groups in positive characteristic as well as over the integers. One of the most interesting aspects of mathematics is to discover and understand connections between objects that from the outset seem unrelated. A very deep such connection has been proposed by Langlands and has become known as the Langlands correspondence. A fundamental theme of this research program is to establish such connections by using geometry. The situation is most interesting when the objects themselves are not geometric but the connection between them is established by geometric means. The joint work with Wilfried Schmid on the Barbasch-Vogan conjecture has this flavour. The other two projects of this research program are directly related to the Langlands correspondence. ***

小行星9803862 该研究计划由三个独立但密切相关的项目组成。 第一个，与威尔弗里德·施密德（Wilfried Schmid）联合，涉及还原李群表示论中的一个重要问题：确定它们的所有酉表示。 他们将使用他们为证明Barbasch-Vogan猜想而开发的几何技术来解决这个问题。 第二个项目，与E.Frenkel，D.Gaitsgory和D.Kazhdan联合，处理朗兰兹结构。 他们将继续他们的工作几何朗兰兹猜想和几何理论的惠特克职能。 目的的第三个项目，联合Mirkovic，是发展几何技术的代表性理论的代数群。 这个项目也被证明是重要的工作几何朗兰兹猜想。 我们的目标是应用他们的方法表示理论的代数群的积极特征以及在整数。 数学最有趣的方面之一是发现和理解从一开始似乎无关的对象之间的联系。 朗兰兹提出了一个非常深刻的这种联系，并被称为朗兰兹对应。 这项研究计划的一个基本主题是通过使用几何建立这种联系。 当物体本身不是几何的，但它们之间的联系是通过几何手段建立起来的时候，这种情况是最有趣的。 联合工作与威尔弗里德施密德的Barbasch-Vogan猜想有这种味道。 该研究计划的其他两个项目与朗兰兹对应直接相关。 ***