Mathematical Sciences: Harmonic Analysis on Reductive Groups

数学科学：约简群的调和分析

• 批准号: 9306138
• 负责人: Jing-Song Huang
• 金额: $ 3.93万
• 依托单位: University of Utah
• 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: 1993-07-01 至 1996-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9306138&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Harmonic; Analysis; Reductive

Huang will study the relationship between representations of a semisimple Lie groups and those of its covering group. He will investigate how their unitary duals and Kazhdan-Lustig conjecture are related. He will also extend the major results of harmonic analysis on symmetric spaces to a certain class of homogeneous spaces which he terms polar. These are homogeneous spaces for which the restricted adjoint representation is polar in the sense of Dadok. 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.

黄将研究的表征之间的关系 半单李群及其覆盖群的半单李群。 他将 研究了它们的酉展开和Kazhdan-Lustig猜想 是有关联的 他还将推广谐波的主要结果 一类齐次对称空间的分析 他称之为极坐标的空间 这些是齐次空间， 其中限制伴随表示在某种意义上是极坐标 关于Dadok 李群理论，以挪威人的荣誉命名 数学家Sophus Lie，一直是 世纪数学。 作为数学工具， 利用系统中固有的对称性， 李群理论对数学产生了深远的影响 本身，特别是在分析和数论，并根据 理论物理学，特别是量子力学和初等 粒子物理学