Mathematical Sciences: Representation Theory For Semisimple Lie Groups

数学科学：半简单李群的表示论

• 批准号: 8802827
• 负责人: Joseph Taylor
• 金额: $ 32.75万
• 依托单位: University of Utah
• 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=8802827&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Representation; Theory; Semisimple

This project is mathematical research in 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. More specifically, the three principal investigators will study algebraic and analytic localizations of representations, in the context of D-modules and Harish-Chandra modules. The overall theme is to get back and forth between various accounting schemes for the representations of a given group. This work involves techniques and ideas from several areas of mathematics, for instance algebraic geometry and complex geometry.

该项目是谎言群体代表理论中的数学研究。 后者的一个合适例子是球体的旋转组。 这样的群体很重要，因为它们发生在许多数学领域（例如几何，微分方程，代数数理论，数学物理学）作为对称组的组。 表示理论允许人们利用对称性解决问题的对称性。 更具体地说，在D模块和Harish-Chandra模块的背景下，三位主要研究人员将研究表示代数和分析的定位。 总体主题是在各种会计方案之间来回探讨给定群体的表示。 这项工作涉及来自数学几个领域的技术和思想，例如代数几何和复杂的几何形状。