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.

该项目是谎言群体代表理论中的数学研究。 后者的一个合适例子是球体的旋转组。 这样的群体很重要，因为它们发生在许多数学领域（例如几何，微分方程，代数数理论，数学物理学）作为对称组的组。 表示理论允许人们利用对称性解决问题的对称性。 更具体地说，彭尼教授将探讨代表理论如何影响复杂分析和几何形状中的基本问题。 一个这样的问题涉及实现方形可集成的共同体学空间中的表示。 这与复杂N空间中无界均匀域的结构理论有关。 要研究的其他问题包括拉普拉斯（Laplace）频谱的关系 - Koszul域的Beltrami操作员与域的几何形状，此类操作员的可溶性特性以及此类域上谐波功能的边界理论。