Mathematical Sciences: Topics in Analysis on Real and P-Adic Lie Groups

数学科学：实李群和 P-进李群分析主题

• 批准号: 9105789
• 负责人: Simon Gindikin
• 金额: $ 9.51万
• 依托单位: Rutgers University New Brunswick
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1991
• 资助国家: 美国
• 起止时间: 1991-06-01 至 1993-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9105789&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Topics; Analysis; Real

Professor Corwin will continue his investigations in harmonic analysis and representation theory for real nilpotent Lie groups and reductive p-adic groups. In the former area he will continue work with F. Greenleaf on homogeneous spaces of nilpotent Lie groups, particularly on problems characterizing the algebra of invariant differential operators for such spaces. Concerning p- adic groups, he will extend his work on supercuspidal representations. This problem is central in questions of representation theory for these groups. Professor Corwin's project involves questions in the representation theory of groups. Group theory is basically the study of symmetry. If a system looks the same from every point in space then the symmetry group contains the group of translations. In particular situations, a knowledge of the abstract group is not enough and one needs to consider concrete realizations of the group of transformations, in other words, a representation.

Corwin教授将继续研究实幂零李群和还原p进群的调和分析和表示论。 在前一个领域，他将继续与 F. Greenleaf 合作研究幂零李群的齐次空间，特别是表征此类空间的不变微分算子代数的问题。 关于 padic 群，他将扩展他在超尖峰表示方面的工作。 这个问题是这些群体的表征理论问题的核心。 Corwin教授的项目涉及群表示论的问题。 群论基本上是对称性的研究。 如果系统从空间中的每个点看起来都相同，则对称组包含平移组。 在特定情况下，仅了解抽象群是不够的，需要考虑变换群的具体实现，换句话说，就是一种表示。