Mathematical Sciences: Nilpotent Conjugacy Classes and Representations of Real Semi-simple Lie Groups

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This career advancement award supports the research of Professor King to study unipotent representations of a given semi- simple Lie group. This will require precise information on the classification and structure of the nilpotent conjugacy classes in the corresponding Lie algebra. The theory of Lie groups, named in honor of the Norwegian mathematician Sophus Lie, has been one of the major themes in twentieth century mathematics. As the mathematical vehicle for exploiting the symmetries inherent in a system, the representation theory of Lie groups has had a profound impact upon mathematics itself, particularly in analysis and number theory, and upon theoretical physics, especially quantum mechanics and elementary particle physics.