Mathematical Sciences: Group Theory and Differential Geometry

数学科学：群论和微分几何

• 批准号: 9625941
• 负责人: Bertram Kostant
• 金额: $ 17.5万
• 依托单位: Massachusetts Institute of Technology
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1996
• 资助国家: 美国
• 起止时间: 1996-07-01 至 2001-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9625941&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Group; Theory; Differential

9625941 Kostant This project deals with research in various topics related to representations and geometric quantization of classical as well as exceptional Lie groups. The investigator proposes to find new approaches to representing the character of an irreducible representation as the Fourier transform of a coadjoint orbit. Singular representations, the quantum cohomology ring of the flag manifold, and representations of a semisimple Lie algebra appearing in its exterior algebra are among the topics to be pursued. Lie groups often arise as symmetry groups. For example, so called unitary Lie groups describe symmetries in elementary particles. Another example is provided by the Carbon 60 molecule, popularly known as the buckyball. Here the full symmetry group turns out to be an exceptional Lie group. There are only finitely many exceptional groups - whereas the number of classical groups are infinite - and much work has been done on how to realize them as subgroups of classical groups.

9625941科斯坦特这个项目涉及与经典李群和例外李群的表示和几何量子化有关的各种主题的研究。研究人员建议找到新的方法来表示不可约表示的特征，如余伴轨道的傅里叶变换。奇异表示、旗形的量子上同调环和半单李代数的表示都是要追求的主题。李群通常以对称群的形式出现。例如，所谓的酉李群描述基本粒子中的对称性。另一个例子是碳60分子，俗称巴克球。在这里，完全对称群变成了一个特殊的李群。只有有限多的例外群--而经典群的数量是无限的--关于如何将它们实现为经典群的子群，已经做了大量的工作。