Mathematical Sciences: Microlocal Character Theory for Representations of Classical Lie Groups

数学科学：经典李群表示的微局部特征理论

• 批准号: 9622610
• 负责人: Tomasz Przebinda
• 金额: $ 2.5万
• 依托单位: University of Oklahoma Norman Campus
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1996
• 资助国家: 美国
• 起止时间: 1996-08-01 至 1999-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9622610&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Microlocal; Character; Theory

Abstract Prezbinda This project is concerned with a microlocal study of characters and matrix coefficients of irreducible unitary representations of classical Lie groups in the context of Howe's theory of real reductive dual pairs. The goal is to understand the characters, matrix coefficients and wave front sets of such representations in terms of the moment maps which occur naturally in that theory. These are the moment maps of classical invariant theory. 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. The mathematical techniques, on which this particular project is based, are also useful in signal processing, data compression and cryptography.

摘要 Prezbinda 该项目涉及在豪实数还原对偶对理论的背景下，对经典李群的不可约酉表示的特征和矩阵系数进行微局域研究。目标是根据该理论中自然发生的矩图来理解此类表示的特征、矩阵系数和波前集。这些是经典不变理论的矩图。 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重要主题之一。 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（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。 这个特定项目所基于的数学技术在信号处理、数据压缩和密码学中也很有用。