Mathematical Sciences: Studies in Representation Theory

数学科学：表示论研究

• 批准号: 9501098
• 负责人: Wilfried Schmid
• 金额: $ 38万
• 依托单位: Harvard University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1995
• 资助国家: 美国
• 起止时间: 1995-06-01 至 2002-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9501098&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Studies; Representation; Theory

DMS-9501098 PI: Schmid Schmid will study representations of reductive groups and Lie algebras from various points of view. He will employ tools from topology, differential geometry, algebraic geometry, and analysis. The expected results and some of the methods developed for the study have applications outside of representation theory. 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.

DMS-9501098 PI：施密德·施密德将从不同的角度研究还原群和李代数的表示。他将使用拓扑学、微分几何、代数几何和分析的工具。预期的结果和为研究开发的一些方法在表象理论之外也有应用。李群理论是以挪威数学家索菲斯·李的名字命名的，一直是20世纪数学的主要主题之一。作为利用系统固有对称性的数学工具，李群的表示理论对数学本身，特别是在分析和数论方面，以及对理论物理，特别是量子力学和基本粒子物理，都产生了深远的影响。