New Methods in the Representation Theory of Finite Groups

9319188 阿尔佩林 该奖项支持在群体表征理论的一些不同方向的研究。 主要调查将适用于结果是最近发现的后果拓扑表示理论的工作块等价。 他还将研究代表理论的有限群的李型使用代数品种和新的想法与复杂性理论的模块从同调表示理论。 最后，他将继续他的研究Hecke代数和研究块等代数的想法从代表性理论的代数。 本文的研究内容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，群是物理、化学、计算机科学和数学中的基本工具。 表示论是确定群结构的重要方法。

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.