Unitary Representations of Reductive P-Adic Groups

还原 P-Adic 群的酉表示

• 批准号: 9803806
• 负责人: Gordan Savin
• 金额: $ 7.2万
• 依托单位: University of Utah
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1998
• 资助国家: 美国
• 起止时间: 1998-07-01 至 2001-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9803806&HistoricalAwards=false
• 关键词: Unitary; Representations; Reductive; Adic; Groups

Abstract Savin DMS-9803806 Muic will investigate unitary representations of classical and certain exceptional reductive p-adic Lie groups, with emphasis on applications in number theory. This will include investigations of reducibility of induced representations and complementary series. He will also investigate a construction of isolated unitary representations. The theory of Lie groups, named after 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 theory of unitary representations of Lie groups has had a profound impact upon mathematics itself, for example in number theory, and upon theoretical physics, especially quantum mechanics and elementary particle physics.

摘要 Savin DMS-9803806 Muic 将研究经典和某些特殊还原 p 进李群的酉表示，重点是在数论中的应用。 这将包括对诱导表征和互补级数的可约性的研究。 他还将研究孤立统一表征的构建。 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大主题之一。 作为利用系统固有对称性的数学工具，李群的酉表示理论对数学本身（例如数论）以及理论物理学（尤其是量子力学和基本粒子物理学）产生了深远的影响。