Mathematical Sciences: Realization of Solvable Lie Groups inL 2 Cohomology Spaces and the Structure of Homogeneous Domains in Cn

数学科学：L 2 上同调空间中可解李群的实现和Cn中齐次域的结构

• 批准号: 8805712
• 负责人: Richard Penney
• 金额: $ 11.37万
• 依托单位: Purdue Research Foundation
• 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: 1988-06-01 至 1991-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8805712&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Realization; Solvable; Lie

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, Professor Penney will explore how representation theory impinges on fundamental questions in complex analysis and geometry. One such question concerns the realization of representations in square integrable cohomology spaces. This is related to the structure theory of unbounded homogeneous domains in complex n-space. Other questions to be investigated include the relation of the spectrum of the Laplace - Beltrami operator of a Koszul domain to the geometry of the domain, the solvability properties of such operators, and the boundary theory of harmonic functions on such domains.

这个项目是数学研究中的表征 李群理论 后者的一个合适的例子是 球面的旋转群。 像这样的团体很重要 因为它们出现在数学的许多领域（例如几何， 微分方程，代数数论，数学 物理学）作为对称群。 表征理论允许 一个是利用对称性解决问题。 更具体地说，彭尼教授将探讨如何 表示论影响了 复杂的分析和几何。 其中一个问题涉及 平方可积上同调表示的实现 空间. 这与无界的结构理论有关 复n-空间中的齐次域 其他问题 研究了拉普拉斯谱的关系 - Beltrami算子的Koszul域的几何 域，此类算子的可解性，以及 调和函数的边界理论。