Mathematical Sciences: Local Harmonic Analysis with Applications to Automorphic Repressentations

数学科学：局部调和分析及其在自同构表示中的应用

• 批准号: 9500880
• 负责人: Diana Shelstad
• 金额: $ 7.5万
• 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: 1995
• 资助国家: 美国
• 起止时间: 1995-06-01 至 1998-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9500880&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Local; Harmonic; Analysis

DMS-9500880 PI: Shelstad Shelstad will investigate the twisted endoscopy of connected reductive algebraic groups over local fields. It is planned to develop descent theory for transfer factors and applying it to some pivotal questions in transfer of twisted orbital integrals. An overall goal is to establish results applicable to stabilization of the adelic twisted trace formula and the study of automorphic representations, especially multiplicity formulas. 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, particularly in analysis and number theory, and upon theoretical physics, especially quantum mechanics and elementary particle physics.

DMS-9500880 PI：Shelstad Shelstad将调查扭曲内窥镜连接约化代数群在当地的领域。 计划发展转移因子的下降理论，并将其应用于扭转轨道积分转移中的一些关键问题。 一个总体目标是建立适用于稳定的adelic扭迹公式和自守表示，特别是多重性公式的研究结果。 李群理论是以挪威数学家Sophus Lie的荣誉命名的，是世纪数学的重要课题之一。 李群表示论作为利用系统中固有对称性的数学工具，对数学本身，特别是分析和数论，以及理论物理学，特别是量子力学和基本粒子物理学产生了深远的影响。