Mathematical Sciences: Unitary Representations in Dolbeault Cohomology

数学科学：Dolbeault 上同调中的酉表示

• 批准号: 9303224
• 负责人: Roger Zierau
• 金额: $ 6.24万
• 依托单位: Oklahoma State University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1993
• 资助国家: 美国
• 起止时间: 1993-05-01 至 1996-10-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9303224&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Unitary; Representations; Dolbeault

Zierau will investigate the realization of singular unitary representation associated to elliptic coadjoint orbits of a semisimple Lie group, i. e. representations on Dolbeault cohomology. He will unitarize these representations using square integrable harmonic forms and the invariant indefinite metric on the orbit. 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.

Zierau将研究与半单李群的椭圆余共轭轨道有关的奇异么正表示的实现，即Dolbeault上同调上的表示。他将使用平方可积调和形式和轨道上的不变不定度规来统一这些表示。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。