9401137 Matumoto Matumoto will investigate analysis concerning the representation theory of real reductive Lie groups. Of particular interest will be use of representation theory in the study of automorphic forms. He will also investigate induced representations from drived functor modules and restrictions of representations. These problems arise naturally in the study of the unitary dual of reductive groups, one of the main subjects of the area. 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 up on mathematics itself, particularly in analysis and number theory, and upon the oretical physics, especially quantum mechanics and elementary particle physics. ***
