Representations of Real Lie Groups, Symmetry Breaking, and Automorphic Forms

实李群、对称破缺和自守形式的表示

• 批准号: 1500644
• 负责人: Birgit Speh
• 金额: $ 30.03万
• 依托单位: Cornell University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2015
• 资助国家: 美国
• 起止时间: 2015-07-01 至 2019-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1500644&HistoricalAwards=false
• 关键词: Representations; Real; Lie; Groups; Symmetry

The investigator will continue long-term research into the study of symmetries and some of their applications. Symmetry is a mathematical concept with direct applications in other sciences such as chemistry, physics, biology, and engineering. The study of algebra, of which this research is a part, is in many ways the study of symmetries. This project aims to advance understanding of important algebraic structures, with potential applications to number theory and theoretical physics.This research project is concerned with symmetry breaking, that is, obtaining representations of a smaller Lie group from the representations of a large reductive semi-simple Lie group. The representations of the large group are usually infinite dimensional, and the representations of smaller groups are related to quotients of the original representation of the large group. Symmetry breaking of representations is far from well understood, and so the constructions and the understanding of examples are very important. This research has applications to number theory and possibly to theoretical physics. Many of the techniques used in these constructions are analytic, and thus some new, interesting, and challenging problems in analysis arise and need to be solved.

研究人员将继续对对称性及其一些应用进行长期研究。 对称性是一个数学概念，可直接应用于化学、物理、生物学和工程学等其他科学。 本研究是代数研究的一部分，在很多方面都是对对称性的研究。 该项目旨在促进对重要代数结构的理解，以及在数论和理论物理方面的潜在应用。该研究项目涉及对称性破缺，即从大型还原半单李群的表示中获得较小李群的表示。 大群的表示通常是无限维的，较小群的表示与大群的原始表示的商相关。 表示的对称性破缺还远未得到很好的理解，因此示例的构造和理解非常重要。这项研究可应用于数论，也可能应用于理论物理学。 这些结构中使用的许多技术都是分析性的，因此分析中出现了一些新的、有趣的和具有挑战性的问题，需要解决。