Professor Przebinda will investigate distribution characters of irreducible admissable representations of classical Lie groups from the viewpoint of microlocal analysis. This will be done in the context of Howe's theory of reductive dual pairs. Three problems are involved in the project: (i) characterize a special class of very singular representations of these groups, (ii) calculate the correspondence of wavefront sets induced in Howe's correspondence of representations, and (iii) investigate the resulting system of differential and microdifferential equations. This research is in the theory of group representations. Group theory is basically the theory of symmetry. To take a simple example, when the system in question is invariant under a change in the position of the origin of space, the group of translations naturally arises. While groups are abstract objects, particular situations demand concrete realizations or "representations" of the symmetry group.
