Unipotent Representations and a Generalization of the Theta Correspondence

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Sahi will construct explicit models for small representations of reductive Lie groups, and use these models to study the decomposition of tensor products of such representations. These models are closely related to the local theta-- correspondence for classical groups, and may be regarded as a natural generalization of this correspondence. The results are expected to have natural global analogues, with applications to the theory of automorphic forms. 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.