Applications of the Bruhat - Tits Building to Representation Theory

Bruhat - 山雀构建在表征理论中的应用

• 批准号: 9801264
• 负责人: Allen Moy
• 金额: $ 8.28万
• 依托单位: Regents of the University of Michigan - Ann Arbor
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1998
• 资助国家: 美国
• 起止时间: 1998-07-15 至 2002-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9801264&HistoricalAwards=false
• 关键词: Applications; Bruhat; Tits; Building; Representation

Allen Moy98 01264A reductive p-adic group is the special collection of symmetries of an arithmetic or geometric object. This study is expected to unravel intricate and fundamental properties of the objects and patterns which are of interest in arithmetic and geometry through the study of these symmetries. One way to understand a group of symmetries is through a representation of its elements as matrices. Representation theory does this in a systematic way. Ultimately the goal is to we are able to construct and classify all representations of the reductive p-adic groups, and from this settle important questions about the underlying geometric object. This is important because so many interesting arithmetic and geometric objects have interesting symmetries that form a reductivep-adic group. This research comes under the umbrella of harmonic analysis on topological groups. Group theory and harmonic analysis are a part of the fundamental underpinnings of certain applications of mathematics to technology in such fields as error correcting codes for efficient and reliable communication and computer imaging, eg. medical imaging, geological imaging or planetary imaging.

艾伦Moy 98 01264约化p-adic群是算术或几何对象的对称性的特殊集合。 这项研究有望通过对这些对称性的研究，揭示算术和几何中感兴趣的物体和图案的复杂和基本性质。 理解一组对称性的一种方法是通过将其元素表示为矩阵。 表征理论以系统的方式做到了这一点。 最终的目标是我们能够构造和分类约化p-adic群的所有表示，并由此解决有关底层几何对象的重要问题。 这一点很重要，因为许多有趣的算术和几何对象都有有趣的对称性，这些对称性形成了一个约化ep-adic群。这项研究属于拓扑群上的调和分析的范畴。 群论和调和分析是数学在技术领域的某些应用的基本基础的一部分，例如用于有效和可靠通信的纠错码和计算机成像。医学成像、地质成像或行星成像。