Mathematical Sciences: Weights for Representations of FiniteGroups

本课题研究有限群的表示理论。首席研究员将致力于建立重量猜想。他还将研究任意有限群的Hecke代数的一般模表示理论，并将研究一些与群结构有关的简单复合体上的系数系统。这个项目是在有限群的表示理论的一般领域。首席研究员将研究这一领域的几个问题，包括权重猜想。对这一猜想的肯定回答将导致这一领域几个长期悬而未决的问题的解决。

This project is concerned with the representation theory of finite groups. The principal investigator will work on establishing the weight conjecture. He will also study the general modular representation theory of Hecke algebras for arbitrary finite groups and will study coefficient systems on some simplicial complexes related to group structure. This project is in the general area of representation theory of finite groups. The principal investigator will examine several problems in this area including the weight conjecture. An affirmative answer to this conjecture would lead to the solution of several long outstanding problems in this area.