Mathematical Sciences: Invariant Distributions on Reductive Groups

数学科学：约简群上的不变分布

• 批准号: 9400797
• 负责人: Rebecca Herb
• 金额: $ 7.4万
• 依托单位: University of Maryland, College Park
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1994
• 资助国家: 美国
• 起止时间: 1994-06-01 至 1997-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9400797&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Invariant; Distributions; Reductive

9400797 Herb Herb will continue her work in the field of representation theory and harmonic analysis on reductive p-adic groups. She will concentrate on studying the most important invariant distributions on these groups, namely tempered characters and orbital integrals. Specific problems which she is interested in include computing Fourier inversion formulas for orbital integrals, and studying reducibility of induced representations for non connected groups. 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. ***

小行星9400797 赫伯将继续她的工作领域的代表性理论和谐波分析约p-adic组。 她将专注于研究这些群体中最重要的不变分布，即调和字符和轨道积分。 具体的问题，她感兴趣的包括计算傅立叶反演公式的轨道积分，并研究reductionof诱导表示非连接组。 李群理论是以挪威数学家Sophus Lie的荣誉命名的，是世纪数学的重要课题之一。 李群表示论作为利用系统中固有对称性的数学工具，对数学本身，特别是分析和数论，以及理论物理学，特别是量子力学和基本粒子物理学产生了深远的影响。 ***