Motive Representation Theory

动机表征理论

• 批准号: 0070716
• 负责人: Thomas Hales
• 金额: $ 18.38万
• 依托单位: Regents of the University of Michigan - Ann Arbor
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2000
• 资助国家: 美国
• 起止时间: 2000-06-01 至 2002-03-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0070716&HistoricalAwards=false
• 关键词: Motive; Representation; Theory

A new type of integration, called motivic integration, has been proposedby M. Konsevitch and developed by Denef and Loeser. They show that manyof the classical properties of p-adic integration can be extended to tothe motivic context. The research of this proposal will adapt motivicintegration to the representation theory and the harmonic analysis ofreductive groups over fields of formal Laurent series in characteristiczero. This new theory will be developed from first principles, startingwith the existence of motivic Haar measures. The starting point of much of modern mathematics is the theory ofintegration, as developed by Isaac Newton, and generations ofmathematicians that have followed him. An unexpected development came in1995, when the mathematician M. Kontsevich developed an entirely new wayto integrate. This new tool will allow mathematicians to significantlyenlarge the scope of mathematics. The research of this grant willaccomplish part of this project, by using this new tool to enlarge thescope of representation theory, a branch of modern algebra.

由M.Konsevitch提出并由Denef和Loeser发展起来的一种新型整合称为Motivic整合。它们表明，p-进积分的许多经典性质可以推广到Motivic上下文中。这一方案的研究将使动机积分适用于表示理论和特征为零的形式洛朗级数的域上的约化群的调和分析。这一新理论将从第一原理发展而来，从动机哈尔度量的存在开始。许多现代数学的起点是由艾萨克·牛顿和他之后的几代数学家发展起来的积分理论。1995年出现了一个意想不到的发展，数学家M·康采维奇开发了一种全新的积分方法。这一新工具将使数学家能够显著扩大数学的研究范围。这项资助的研究将完成这一项目的一部分，通过使用这一新工具来扩大现代代数的一个分支--表示论的范围。