Mathematical Sciences: Representations of Finite Reductive Groups: A Characteristic Free Approach Through q-Deformations

本课题研究一般线性群的表示理论及其量化。首席研究员将研究与Weyl群相关的Hecke代数，努力扩展q-Schur代数的工作，并将其应用于其他Lie型群。本研究是在有限经典群的表示理论的一般领域。群论在其他数学和科学领域的主要应用之一是表示理论，有限经典群是有限单群的主要来源。

This project is concerned with the representation theory of general linear groups and their quantizations. The principal investigator will investigate the Hecke algebras associated with Weyl groups in an effort to extend the work on q-Schur algebras and apply it to other groups of Lie type. This research is in the general area of the representation theory of finite classical groups. One of the main applications of group theory to other mathematical and scientific fields is in representation theory, and finite classical groups are a primary source of finite simple groups.