Mathematical Sciences: Minimal K-types and Hecke Algebra Isomorphisms for p-adic Groups

数学科学：p-adic 群的最小 K 型和 Hecke 代数同构

• 批准号: 8701429
• 负责人: Allen Moy
• 金额: $ 2.94万
• 依托单位: University of Washington
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1987
• 资助国家: 美国
• 起止时间: 1987-06-01 至 1990-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8701429&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Minimal; types; Hecke

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, Lie theory has had a profound impact upon mathematics itself and theoretical physics, especially quantum mechanics and elementary particle physics. A major application of Lie thoery is to algebraic number theory, for which an understanding of the p-adic theory is essential. Professor Moy is possibly the strongest young researcher in this area. His recent work on minimal K-types and Hecke isomorphism provides some of the most important advances in the representation theory of p-adic groups in a long time. Moy plans to continue the development of this theory. His proposed work generalizes the most current results from the real theory to the p-adic case. Professor Moy envisages application to the crucial discrete series of representations.

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，李理论 对数学本身和理论产生了深远的影响 物理学，特别是量子力学和基本粒子 物理学 李理论的一个主要应用是代数数 理论，其中对p-adic理论的理解是 具有本质意义 莫教授可能是最强壮的 这方面的研究者。 他最近在最小K型和 Hecke同构提供了一些最重要的进展 p-adic群的表示理论。 Moy 计划继续发展这一理论。 他提出的 工作概括了最新的结果从真实的理论， p-adic的例子 莫教授设想应用于 关键的离散表示系列。