Mathematical Sciences: Representation Theory of Reductive P-Adic Groups

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DMS-9500973 PI: Moy Moy will investigate various aspects of the representation theory of p-adic reductive groups. This will include investigations into the behavior of characters in which the local character expansion of a representation is shown to be connected to certain representations of compact open subgroups appearing in the representation, and the development of the theory of minimal K-types for reductive p-adic groups based on the results of unrefined minimal K-types. 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.