Mathematical Sciences: Integral Geometry and Analysis on Affine Symmetric Spaces

数学科学：积分几何和仿射对称空间分析

• 批准号: 9202049
• 负责人: Simon Gindikin
• 金额: $ 9.2万
• 依托单位: Rutgers University New Brunswick
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1992
• 资助国家: 美国
• 起止时间: 1992-06-01 至 1995-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9202049&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Integral; Geometry; Analysis

Gindikin will investigate multidimensional problems in integral geometry and analysis on affine symmetric spaces. The first part of this project will be to construct local inversion formulas and to relate them to the representation theory of Lie groups. The second part of the proposal will consider analysis on homogeneous cones and Siegel domains with an aim towards developing explicit realizations of results from representation theory, including Plancherel measure and spherical functions. 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 and theoretical physics, especially quantum mechanics and elementary particle physics.

Gindikin 将研究积分几何中的多维问题以及仿射对称空间的分析。 该项目的第一部分将是构造局部反演公式并将其与李群的表示理论联系起来。 该提案的第二部分将考虑对齐次锥体和西格尔域进行分析，旨在开发表示论结果的明确实现，包括 Plancherel 测度和球面函数。 李群理论以挪威数学家索弗斯·李的名字命名，一直是二十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，李群的表示论对数学本身和理论物理学，特别是量子力学和基本粒子物理学产生了深远的影响。