Mathematical Sciences: Representations of Classical Groups and Hecke Algebras

在这项研究中，首席研究员将继续 进一步发展了一般线性群的表示理论。 在 特别是，有很好的理由假设，新的光可以是 在描述中， 作为一个特殊的情况下，这个理论的特点， 主要研究者和他的同事的结构。 拟议工作的主要目标是调查其他 经典团体扩展了由 在以前的工作中担任首席研究员，目的是 获得这些的简单表示的分类 组 为此，与Weyl群相关的Hecke代数 必须加以研究。 鉴于这些代数在 整个领域，这可能是感兴趣的本身，提供 更详细的信息Hecke代数适用于相关 话题

In this research the principal investigator will pursue further the representation theory of general linear groups. In particular, there is good reason to suppose that new light can be shed on the classical theory of representations in the describing characteristic by subsuming this theory as a special case of the constructions of the principal investigator and his coworker. The major goal of the proposed work is to investigate other classical groups extending the techniques developed by the principal investigator in previous work, with the aim of obtaining a classification of the simple representations of these groups. For this, Hecke algebras associated with Weyl groups have to be studied. In view of the key role of these algebras in the whole field this might be of interest by itself, providing more detailed information on Hecke algebras applicable to related topics.