The PI proposes to continue his investigations on the holomorphic aspects of representations of Lie groups. An emphasis will be taken towards applications to automorphic forms and harmonic analysis. In particular, one objective is to obtain estimates on the Fourier coefficients of automorphic forms.
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.
