Unitary Representations of Reductive P-Adic Groups

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Abstract Savin DMS-9803806 Muic will investigate unitary representations of classical and certain exceptional reductive p-adic Lie groups, with emphasis on applications in number theory. This will include investigations of reducibility of induced representations and complementary series. He will also investigate a construction of isolated unitary representations. The theory of Lie groups, named after 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 theory of unitary representations of Lie groups has had a profound impact upon mathematics itself, for example in number theory, and upon theoretical physics, especially quantum mechanics and elementary particle physics.