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

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Professor Salamanca Riba will investigate various topics in the theory of unitary representations of reductive Lie groups. Firstly, she will attempt to complete a proof of a conjecture of Zuckerman that certain Harish-Chandra modules are isomorphic to Zuckerman functor modules. In addition she will consider other generalizations of the above conjecture. For example, in certain cases Barbasch and Vogan have conjectured that these derived functor modules are obtained from a special unipotent representation. Professor Salamanca Riba will attempt to prove this. The research project being described here is in group representation theory. Groups usually arise as transformations which preserve the structure of a system under investigation, as for example the group of rotations around the center preserves a sphere. In specific applications a concrete realization of the abstract group, or representation, is often needed. These are the objects which are being studied here.