Mathematical Sciences: Representations of Classical Groups and Hecke Algebras

在本研究中，主要研究者将进一步探讨一般线性群的表示理论。特别是，有很好的理由假设，通过将经典表征理论作为主要研究者和他的同事的结构的特殊情况纳入这一理论，可以为描述特征中的表征理论提供新的思路。这项工作的主要目标是研究其他经典群，扩展由首席研究员在以前的工作中开发的技术，目的是获得这些群的简单表示的分类。为此，必须研究与Weyl群相关的Hecke代数。鉴于这些代数在整个领域的关键作用，这本身可能会引起人们的兴趣，提供更多适用于相关主题的赫克代数的详细信息。

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.