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将研究积分几何形状的多维问题，并分析仿射对称空间。 该项目的第一部分将是构建局部反转公式，并将其与谎言群体的代表理论联系起来。 该提案的第二部分将考虑对均质锥和西格尔领域的分析，目的是旨在从代表理论（包括plancherel测度和球形功能）中对结果进行明确的实现。 以纪念挪威数学家索菲斯谎言而命名的谎言理论一直是20世纪数学的主要主题之一。 作为利用系统固有的对称性的数学工具，谎言组的表示理论对数学本身和理论物理学，尤其是量子力学和基本粒子物理学产生了深远的影响。