Mathematical Sciences: Representation Theory

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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.