Mathematical Sciences: Representations of p-adic Groups

数学科学：p-adic 群的表示

• 批准号: 9304284
• 负责人: Mark Reeder
• 金额: $ 4万
• 依托单位: University of Oklahoma Norman Campus
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1993
• 资助国家: 美国
• 起止时间: 1993-06-01 至 1995-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9304284&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Representations; adic; Groups

Professor Reeder will continue his work on the representations of p-adic algebraic groups. He will seek explicit results about the representations containing an Iwahori-fixed vector. This work exploits the interplay between p-adic harmonic analysis and complex algebraic geometry. This project falls into the general area of arithmetic geometry -a subject that blends two of the oldest areas of mathematics: number theory and geometry. This combination has proved extraordinarily fruitful - having recently solved problems that withstood generations. Among its many consequences are new error correcting codes. Such codes are essential for both modern computers (hard disks) and compact disks.

Reeder教授将继续他在p-进代数群表示方面的工作。他将寻求关于包含Iwahori固定向量的表示的明确结果。这项工作利用了p-进调和分析和复代数几何之间的相互作用。这个项目属于算术几何的一般领域--一个融合了数论和几何这两个最古老的数学领域的学科。事实证明，这种结合非常有成效--最近解决了几代人经受住的问题。在其众多后果中，有一种是新的纠错码。这种代码对于现代计算机(硬盘)和光盘都是必不可少的。