Mathematical Sciences: Research in Representation Theory andAutomorphic Forms

数学科学：表示论和自守形式研究

• 批准号: 9302723
• 负责人: Nolan Wallach
• 金额: $ 25.19万
• 依托单位: University of California-San Diego
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1993
• 资助国家: 美国
• 起止时间: 1993-07-01 至 1997-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9302723&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Research; Representation; Theory

Wallach will investigate invariant differential operators acting on invariant distributions on a reductive Lie algebra, diagonal invariants and harmonics for Coxeter groups, Automorphic forms related to the error term in asymptotic behavior of lattice point problem and the Kloosterman-Selberg zeta function. Wallach will also work to develop parallel computer algorithms for the calculation of Groebner bases and a general software package to be used in the study of diagonal invariants and harmonics for Coxeter groups. 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.

瓦拉赫将研究不变微分算子 作用于约化李代数上的不变分布， Coxeter群的对角不变量和调和函数，自守 格的渐近性态中与误差项有关的形式 点问题和Kloosterman-Selberg zeta函数。 Wallach 还将致力于开发并行计算机算法， Groebner基的计算和通用软件包， 可用于对角不变量和谐波的研究， 考克斯特集团。 李群理论，以挪威人的荣誉命名 数学家Sophus Lie，一直是 世纪数学。 作为数学工具， 利用系统中固有的对称性， 李群的表示理论对 数学本身，特别是在分析和数字方面， 理论和理论物理学，特别是量子 力学和基本粒子物理学。