Mathematical Sciences: Representation Theory

该奖项支持华盛顿大学教授罗纳德欧文在李群和李代数方面的研究。欧文博士的项目是研究某些代数主题的基础最近的工作表示理论的复杂半单李代数和真实的还原李群。李理论中许多重要的表示都是有限长的，并且都在有限长模范畴中。这些范畴带有大量额外的代数结构，如平移函子或过滤特征标理论。欧文教授将更详细地研究这些特征及其后果。任何时候，只要有操作可以撤销，也可以完成，就有一个组存在。在上个世纪，人们首次系统地研究了群论。当挪威数学家索菲斯·李（Sophus Lie）证明群论以一种非常自然的方式应用于微分方程的研究时，群论的力量和意义得到了所有数学家的认可。这里支持的工作是李的第一个开创性工作的现代延续。

This award supports the research in Lie groups and Lie algebras of Professor Ronald Irving of the University of Washington. Dr. Irving's project is to study certain algebraic topics underlying recent work in the representation theory of complex semisimple Lie algebras and real reductive Lie groups. Many important representations in Lie theory have finite length and lie in categories of finite length modules. These categories carry a great deal of additional algebraic structure, such as translation functors or a filtered character theory. Professor Irving will study these features and their consequences in greater detail. Any time there are operations that may be undone as well as done, there is a group present. Groups were first studied systematically in the last century, and when the Norwegian mathematician Sophus Lie showed that group theory applied in a very natural way to the study of differential equations, the strength and significance of group theory became recognized by all mathematicians. The work supported here is a modern continuation of that first pioneering work of Lie.