Mathematical Sciences: Invariant Distributions on Reductive Groups

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9400797 Herb Herb will continue her work in the field of representation theory and harmonic analysis on reductive p-adic groups. She will concentrate on studying the most important invariant distributions on these groups, namely tempered characters and orbital integrals. Specific problems which she is interested in include computing Fourier inversion formulas for orbital integrals, and studying reducibility of induced representations for non connected groups. 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. ***