This project is mathematical research in the representation theory of Lie groups. A suitable example of the latter is the group of rotations of a sphere. Groups like this are important because they occur in many areas of mathematics (e.g. geometry, differential equations, algebraic number theory, mathematical physics) as groups of symmetries. Representation theory allows one to take advantage of symmetries in solving problems. More specifically, Professor Wolf will complete work on an extension of the theory of Harish - Chandra to general real semisimple Lie groups. He will complete the development of certain important consequences of the recently developed duality between two constructions of Harish - Chandra modules. He will complete and apply the results of a project that shows in a rather explicit way how all the usual analytic and geometric constructions of admissible representations are equivalent for reductive Lie groups. A further aspect of his research plan concerns the interplay between representation theory and complex analysis.
