Unipotent Representations and a Generalization of the Theta Correspondence

单能表示和 Theta 对应的推广

• 批准号: 9317838
• 负责人: Siddhartha Sahi
• 金额: $ 6.48万
• 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: 1993
• 资助国家: 美国
• 起止时间: 1993-07-01 至 1996-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9317838&HistoricalAwards=false
• 关键词: Unipotent; Representations; Generalization; Theta; Correspondence

Sahi will construct explicit models for small representations of reductive Lie groups, and use these models to study the decomposition of tensor products of such representations. These models are closely related to the local theta-- correspondence for classical groups, and may be regarded as a natural generalization of this correspondence. The results are expected to have natural global analogues, with applications to the theory of automorphic forms. 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.

Sahi将为约化李群的小表示构造显式模型，并使用这些模型来研究这种表示的张量积的分解。这些模型与经典群的局部theta对应关系密切，可以看作是这种对应关系的自然推广。这些结果有望具有自然的全局相似性，并应用于自同构形式理论。李群理论是以挪威数学家索菲斯·李的名字命名的，一直是20世纪数学的主要主题之一。作为利用系统固有对称性的数学工具，李群的表示理论对数学本身，特别是在分析和数论方面，以及对理论物理，特别是量子力学和基本粒子物理，都产生了深远的影响。