Motive Representation Theory

M.提出了一种新型的整合，称为动机整合。Konsevitch，由Denef和Loeser开发。 他们表明，p-adic积分的许多经典性质可以扩展到motivic背景。 这一建议的研究将使动机整合适应于特征为零的形式洛朗级数域上的约化群的表示论和调和分析。 这一新理论将从第一性原理出发，从motivic Haar测度的存在性出发。许多现代数学的起点是积分理论，由艾萨克·牛顿和几代追随他的数学家发展起来。 1995年出现了一个意想不到的发展，数学家M。Kontsevich开发了一种全新的整合方式。 这一新工具将使数学家们大大扩大数学的范围。 本基金的研究将完成该项目的一部分，利用这一新的工具来扩大现代代数的一个分支--表示论的研究范围。

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.