This award provides partial support for approximately twenty two reciprocal research visits by US and West German mathematicians, coordinated by Jonathan L. Alperin of the University of Chicago and Gerhard Michler of the University of Essen. The research activities of the visitors fall into six areas: integral representation theory, character theory, module methods (Clifford theory, complexity and vertices of simple modules,) computer methods, Clifford matrices and the representation theory of algebras. The Deutsche Forschungsgemeinschaft (DFG), the West German analog of NSF, is supporting a very large continuing program in representation theory of groups and algebras. Under this program, the DFG brings large numbers of mathematicians from around the world to West Germany for extended periods to collaborate and communicate with German mathematicians and others. Over the next two years, the DFG will support the living expenses of twelve U.S. visitors to West Germany and travel expenses for ten Germans coming to the U.S. to work in this area of mathematics. NSF will provide complementary support for the U.S. mathematicians' travel costs and partial support of the German visitors' expenses in the U.S. This award, shared by NSF's Division of Mathematical Sciences, continues support provided in 1987 and 1988 for 26 research visits that proved to be highly productive and mutually beneficial. The past and future visitors are an outstanding collection of mathematicians working in an area that is very active and important in both the U.S. and West Germany.
