Mathematical Sciences: Representation Theory

该奖项支持华盛顿大学罗纳德·欧文教授在李群和李代数方面的研究。欧文博士的项目是研究复半单李代数和实约化李群的表示理论中的某些代数主题。李理论中的许多重要表示都是有限长度的，它们都存在于有限长度模范畴中。这些范畴带有大量额外的代数结构，例如翻译函子或过滤特征理论。欧文教授将更详细地研究这些特征及其后果。任何时候，只要有既可以撤消又可以完成的操作，就会有一群人在场。群论在上个世纪首次被系统地研究，当挪威数学家索菲斯·李证明群论以一种非常自然的方式应用于微分方程式的研究时，群论的力量和重要性得到了所有数学家的认可。这里支持的工作是LIE第一次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.