Mathematical Sciences: Groups of Lie Type - Group Proposal

这个项目是关于李氏理论的研究。它将涵盖这一领域的广泛主题，包括自然特征中李型有限群及其相关代数群的表示理论；李型有限群的特征标理论；李型群的结构和几何；以及轨道的几何和与李群表示的联系。这个项目属于群论的一般领域。群是定义了乘法的代数对象。这样的对象在数学的许多分支中都很重要，在物理、化学和计算机科学等其他领域也变得越来越重要。该项目提供的资金将通过可能的某些合作努力来提高这一领域的研究质量和水平。它还将为研究生提供资金。

This project is concerned with research in Lie theory. It will cover a broad spectrum of topics in this field including representation theory of finite groups of Lie type and associated algebraic groups in the natural characteristic; the character theory of finite groups of Lie type; the structure and geometry of groups of Lie type; and the geometry of orbits and connections with Lie group representations. This project is in the general area of group theory. A group is an algebraic object with a multiplication defined on it. Such objects are important in many branches of mathematics and are becoming increasingly important in other areas such as physics, chemistry and computer science. This project provides funding that will enhance the quality and level of research in this area by making possible certain collaborative efforts. It will also provide funding for graduate students.