DMS-9505055 PI: Brylinski Brylinski will continue her research on the quantization of nilpotent orbits. The main thrust of the project is to investigate the symplectic and algebraic geometry of nilpotent orbits and to find ways to quantize these orbits within the broad scheme of geometric quantization. The outcome will be the construction of geometric models of unitary representations. This work will result in a better understanding of geometric quantization, quantization in general, and the geometry and invariant theory of nilpotent orbits. 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.
