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和仿射对称空间的分析。本课题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的分析，旨在开发包括Plancherel测度和球面函数在内的表示理论结果的明确实现。李群理论是为了纪念挪威数学家索夫斯·李而命名的，它一直是20世纪数学的主要主题之一。李群表示理论作为探索系统对称性的数学工具，对数学本身和理论物理，特别是量子力学和基本粒子物理产生了深远的影响。