Mathematical Sciences: The Structure and Representations of Algebraic Groups and Associated Finite Groups

本研究关注的是结构和 代数群和相关有限群的表示。 主要研究者将根据 单可约子群结构与嵌入 代数群;工作链接的子群结构 有限群到代数群;研究 域上对称群的表示理论 正特征;并研究表示有限 定义特征的域上的Lie型群。 一个群是一个具有单一运算的代数结构。 它出现在数学的许多领域，以及，物理学和 化学. 有限群的基本构造块是 有限单群 数学中的一个重要成果是 过去的十年是有限简单的分类 团体，这将需要10，000至15，000的证明 日记页。 这项研究旨在利用这一 在任意有限群的研究中分类。

This research is concerned with the structure and representations of algebraic groups and associated finite groups. The principal investigator will establish results on the structure and embedding of reductive subgroups of simple algebraic groups; work on linking the subgroup structure of finite groups to that of algebraic groups; study the representation theory of the symmetric groups over fields of positive characteristic; and study representations of finite groups of Lie type over a field of the defining characteristic. A group is an algebraic structure with a single operation. It appears in many areas of mathematics, as well as, physics and chemistry. The fundamental building blocks of finite groups are finite simple groups. One of the major results in mathematics of the past decade is the classification of the finite simple groups, the proof of which would require 10,000 to 15,000 journal pages. This research is aimed at using this classification in the study of arbitrary finite groups.