Mathematical Sciences: Cohomology of G/P and Representation Theory of G, for Real Reductive Lie Groups and Generalizations

数学科学：G/P 的上同调和 G 的表示论，用于实数还原李群和推广

• 批准号: 9302702
• 负责人: Luis Casian
• 金额: --
• 依托单位: Ohio State University Research Foundation -DO NOT USE
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1993
• 资助国家: 美国
• 起止时间: 1993-06-15 至 1996-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9302702&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Cohomology; Representation; Theory

Casian will study the problem of computing the cohomology of the flag variety for real reductive Lie groups, the cup product and Weyl group action, using the representation theory of the group. He will investigate the problem of determining which Schubert cells contribute to the non torsion part in homology. He will also investigate similar problems in the Kac-Moody setting. 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, particularly in analysis and number theory, and upon theoretical physics, especially quantum mechanics and elementary particle physics.

Casian将利用群的表示理论研究实约化李群的FLAG簇的上同调、杯积和Weyl群作用的计算问题。他将研究确定哪些舒伯特细胞对同调中的非扭转部分有贡献的问题。他还将在Kac-Moody的背景下调查类似的问题。李群理论是以挪威数学家索菲斯·李的名字命名的，一直是20世纪数学的主要主题之一。作为利用系统固有对称性的数学工具，李群的表示理论对数学本身，特别是在分析和数论方面，以及对理论物理，特别是量子力学和基本粒子物理，都产生了深远的影响。