Mathematical Sciences: Unitary Representations of Lie Groups and Derived Functor Modules

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DMS-9510608 PI: Salamanca Riba Salamanca Riba will investigate the relation between certain irreducible unitary Harish-Chandra modules for a group and Zuckerman functor modules derived from a one dimensional unitary representation of a subgroup. She will also consider the problem of classifying all genuine unitary representations of the metaplectic group. In particular, she will consider the Adams-Barbasch correspondence between these representations and a set of unitary representations of certain inner forms of the metaplectic group and determine if the representations go to Zuckerman functor modules under this map. 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.