Mathematical Sciences: Automorphic Representations, L-Packets and Theta Liftings

数学科学：自守表示、L 包和 Theta 提升

• 批准号: 9106194
• 负责人: Jonathan Rogawski
• 金额: $ 8.65万
• 依托单位: University of California-Los Angeles
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1991
• 资助国家: 美国
• 起止时间: 1991-07-01 至 1995-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9106194&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Automorphic; Representations; Packets

This award supports the research of Professor J. Rogawski to work in automorphic functions. He intends to work on the relations between L-packets and theta liftings for unitary groups. He intends to first study the quasi-split unitary group U(3) and then try to extend these results to general unitary groups. Modular forms arose out of Non-Euclidean geometry in the middle of the nineteenth century. Both mathematicians and physicists have thus long realized that many objects of fundamental importance are non-Euclidean in their basic nature. This field is principally concerned with questions about the whole numbers, but in its use of geometry and analysis, it retains connection to its historical roots and thus to problems in areas as diverse as gauge theory in theoretical physics and coding theory in information theory.

该奖项支持 J. Rogawski 教授在自守函数方面的研究。 他打算研究酉群的 L 包和 theta 提升之间的关系。 他打算首先研究准分裂酉群 U(3)，然后尝试将这些结果推广到一般酉群。 模形式产生于十九世纪中叶的非欧几里得几何学。 数学家和物理学家很早就认识到，许多具有根本重要性的物体的基本性质都是非欧几里得的。 该领域主要关注有关整数的问题，但在几何和分析的使用中，它保留了与其历史根源的联系，从而与理论物理学中的规范理论和信息论中的编码理论等不同领域的问题保持联系。