Mathematical Sciences: Representation Theory of Reductive Groups

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This research project is in the field of representation theory and harmonic analysis on real reductive Lie groups and other reductive algebraic groups. Principal investigator Adams will continue his study of Arthur's conjectures and unipotent representations for real groups. Also, Adams' research will involve an examination of the role of L-groups in reductive dual pairs, both for real groups, and over finite and p-adic fields. Investigator Herb will continue her study of the Schwarz space for semisimple Lie groups with infinite center. These problems require showing how wave packets patch together at points where different series of tempered representations overlap. Also, this research involves an examination of supertempered representations in the context of Fourier inversion of orbital integrals for p- adic groups. This research is in the general area of modern analysis and, in particular, in obtaining the representations of groups of transformations on spaces.