Cohomology & Modular Representation Theory of Finite & Algebraic Groups

9401292本项目涉及代数及相关有限群的模表示理论。主要研究者感兴趣的是著名的Lusztig猜想对特征标大于Coxeter数的不可约表示的特征标的解。这个问题的一个成功的解决方案将对有限群产生许多影响。主要研究者的工作已经在代数群的表示理论和有限维代数理论之间建立了重要的联系。主要研究人员还将研究与有限群、李代数和量子群有关的问题。所支持的研究涉及有限群的表示理论。群是用于研究变换的代数对象。正因为如此，小组是物理、化学和计算机科学以及数学中的基本工具。表象理论是确定群结构的重要方法。

9401292 Parshall This project is concerned with the modular representation theory of algebraic and associated finite groups. The principal investigators are interested in a solution of the famous conjecture of Lusztig for characters of the irreducible representations in characteristic larger than the Coxeter number. A successful solution to this problem would have many ramifications for finite groups. The work of the principal investigators has already established an important connection between the representation theory of algebraic groups and the theory of finite dimensional algebras. The principal investigators will also work on problems concerning finite groups, Lie algebras, and quantum groups. The research supported concerns the representation theory of finite groups. A group is an algebraic object used to study transformations. Because of this, groups are a fundamental tool in physics, chemistry and computer science as well as mathematics. Representation theory is an important method for determining the structure of groups.