Mathematical Sciences: Representation Theory of P-ADIC Groups

数学科学：P-ADIC群的表示论

• 批准号: 9203933
• 负责人: Allen Moy
• 金额: $ 6.5万
• 依托单位: Regents of the University of Michigan - Ann Arbor
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1992
• 资助国家: 美国
• 起止时间: 1992-07-01 至 1995-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9203933&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Representation; Theory; ADIC

Moy will continue his joint work with Barbasch investigating the unitary dual of a reductive p-adic group and will investigate with Hales certain ways to establish what is called a uniform germ expansion for orbital integrals. The research in unitarity, with a goal of classifying all unitary representations, will be to investigate certain basic representations called unipotent representations. The investigations in uniform germ expansions will be to find a way for determining whether two spaces of distributions are equal. The theory of Lie groups, named in honor of the Norwegian mathematician Sophus Lie, has been one of the major themes in twentieth century mathematics. As the mathematical vehicle for exploiting the symmetries inherent in a system, the representation theory of Lie groups has had a profound impact upon mathematics itself, particularly in analysis and number theory, and upon theoretical physics, especially quantum mechanics and elementary particle physics.

Moy将继续与Barbasch共同调查 约化p-adic群酉对偶，并将研究 用黑尔斯的某些方法来建立所谓的制服 轨道积分的芽展开 关于么正性的研究， 目标是对所有酉表示进行分类， 来研究一些叫做幂幺的基本表示 表示。 一致芽扩张的研究 将找到一种方法来确定两个空间的 分配是平等的。 李群理论，以挪威人的荣誉命名 数学家Sophus Lie，一直是 世纪数学。 作为数学工具， 利用系统中固有的对称性， 李群的表示理论对 数学本身，特别是在分析和数字方面， 理论和理论物理学，特别是量子 力学和基本粒子物理学。