Mathematical Sciences: Representation Theory of Real Reductive Groups, L-groups and Reductive Dual Pairs

数学科学：实数还原群、L-群和还原对偶的表示论

• 批准号: 9401074
• 负责人: Jeffrey Adams
• 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: Standard Grant
• 财政年份: 1994
• 资助国家: 美国
• 起止时间: 1994-06-01 至 1997-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9401074&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Representation; Theory; Real

9401074 Adams Adams will continue his work on the representation theory of real reductive Lie groups, with particular focus on the representation correspondence arising from real reductive dual pairs, generalizing recent work on complex groups and the dual pairs (O(p,q),Sp(2n,R) with p+q=2n+1. He will also investigate questions arising in connection with Arthur's conjectures. 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 up on mathematics itself, particularly in analysis and number theory, and upon the oretical physics, especially quantum mechanics and elementary particle physics. ***

9401074亚当斯 亚当斯将继续他的工作表示理论的真实的还原李群，特别侧重于代表性的对应关系所产生的真实的还原对偶，概括最近的工作复杂的群体和对偶对（O（p，q），Sp（2n，R）与p+q=2n+1。 他还将调查与亚瑟的肖像有关的问题。 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。 ***