Mathematical Sciences: Representation Theory and Automorphic Forms

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9401176 Speh/Barbasch Speh will continue her joint work with Rohlfs on cuspidal cohomology. She also will investigate the analytic torsion of locally symmetric spaces. In joint work the PI's will study the residual spectrum of the split orthogonal and symplectic group. Barbasch will continue his research on unipotent representations for real groups, in particular their character theory and unitarity. He also will study spherical unitary dual for split p- adic groups. 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. ***