Mathematical Sciences: Representations of Discrete Rational Nilpotent Groups

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Pfeffer will extend the classical Kirillov theory of real nilpotent Lie groups to the non-type-I setting. The basic technique involved exploits the structure of co-adjoint orbits closures in the dual of the associated Lie algebra. These closures are cosets of subgoups of the Lie algebra dual which annihilate ideals in the Lie algebra. Pfeffer will investigate whether the space of co-adjoint orbit closures is homeomorphic to the primitive ideal space. 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.