Mathematical Sciences: Studies in Representation Theory

数学科学：表示论研究

• 批准号: 9204511
• 负责人: Wilfried Schmid
• 金额: $ 41.45万
• 依托单位: Harvard University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1992
• 资助国家: 美国
• 起止时间: 1992-06-01 至 1995-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9204511&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Studies; Representation; Theory

Schmid and Bernstein plan to continue their study of the representation theory of reductive groups and Lie algebras from a variety of points of view. They plan to employ tools from topology, algebraic geometry, differential geometry, and analysis. The expected results, in turn, will have applications to geometry, number theory, and analysis. 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 and theoretical physics, especially quantum mechanics and elementary particle physics.

施密德和伯恩斯坦计划继续他们的研究 约化群和李代数的表示论 各种各样的观点。 他们计划使用来自 拓扑学，代数几何，微分几何， 分析. 预期的结果，反过来， 几何学数论和分析 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 数学本身和理论物理学，特别是 量子力学和基本粒子物理学。