New Methods in the Representation Theory of Finite Groups

9319188 Alperin这个奖项支持了群体表征理论中许多不同方向的研究。主要研究者将把拓扑学中最近发现的结果应用到块等价的表示理论中。他还将研究李型有限群的表示理论，利用代数变异和与同调表示理论中模的复杂性理论相关的新思想。最后，他将继续他对赫克代数的研究，并利用代数表示理论的思想研究赫克代数的块。本研究支持有限群的表示理论。群是用来研究变换的代数对象。正因为如此，分组是物理、化学、计算机科学以及数学的基本工具。表征理论是确定群体结构的重要方法。

9319188 Alperin This award supports research on a number of different directions in group representation theory. The principle investigator will apply results which are consequences of recent discoveries in topology to representation theory in work on block equivalences. He will also study the representation theory of finite groups of Lie type using algebraic varieties and new ideas associated with the complexity theory of modules from homological representation theory. Finally, he will continue his study of Hecke algebras and study the blocks of such algebras with ideas from the representation theory of algebras. 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.