Mathematical Sciences: Unipotent Representations for Reductive Groups

数学科学：还原群的单能表示

• 批准号: 8803500
• 负责人: Dan Barbasch
• 金额: $ 6.86万
• 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: 1988
• 资助国家: 美国
• 起止时间: 1988-07-01 至 1992-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8803500&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Unipotent; Representations; Reductive

The principal investigator plans to work on problems in mathematical analysis concerning the representation theory of Lie groups. A suitable example of the latter is the group of rotations of a sphere. Groups like this are important because they occur in many areas of mathematics ( e.g. geometry, differential equations,algebraic number theory, mathematical physics ) as groups of symmetries. Representation theory allows one to take advantage of symmetries in solving problems. The building blocks for representation theory are the irreducible representations, particularly the irreducible unitary representations. The principal investigator will work toward classifying these representations for certain classes of Lie groups. More specifically, he will continue work on determining the character theory and unitarity of the unipotent representations of reductive groups. This will provide significant insight into the unitary dual and certain problems in the theory of automorphic forms.

首席研究员计划解决 数学分析的代表性理论 李群。 后者的一个合适的例子是以下基团： 球体的旋转。 像这样的团体很重要，因为 它们出现在数学的许多领域（例如几何， 微分方程，代数数论，数学 物理学）作为对称群。 表征理论允许 一个是利用对称性解决问题。 表示论的基石是 不可约表示，特别是不可约 酉表示 首席研究员将在 对这些表示进行分类， 李群。更具体地说，他将继续致力于 确定幂幺的特征标理论和么正性 约化群的表示这将提供 重要的洞察力，以单一的双重和某些问题， 自守形式理论。