Applications of the Bruhat - Tits Building to Representation Theory

Allen Moy98 01264A约化p-Add群是算术或几何对象的对称性的特殊集合。通过对这些对称性的研究，这项研究有望揭开对算术和几何感兴趣的物体和图案的复杂而基本的性质。理解一组对称的一种方法是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。最终的目的是我们能够构造和分类约化p-进群的所有表示，并由此解决关于潜在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具有有趣的对称性，这些对称性形成了一个约简半群。本研究属于拓扑群调和分析的范畴。群论和调和分析是数学对技术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，例如。医学成像、地质成像或行星成像。

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.