Motive Representation Theory

Konsevitch提出了一种新的整合类型，称为动机整合，由Denef和Loeser发展。它们表明p进积分的许多经典性质可以推广到动机环境中。本文的研究将动机积分引入到表征理论和特征零点形式洛朗级数域上约化群的调和分析中。这个新理论将从第一性原理出发，从哈尔测度的存在开始发展。许多现代数学的起点都是由艾萨克·牛顿（Isaac Newton）及其后继几代数学家提出的积分理论。1995年出现了一个意想不到的进展，数学家M. Kontsevich开发了一种全新的积分方法。这个新工具将使数学家能够大大扩大数学的范围。本基金的研究将完成本计划的一部分，利用这个新工具来扩大表征理论（现代代数的一个分支）的范围。

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.