From April 1, 1984 until March 31, 1991 the Deutsche Forschungsgemeinschaft has sponsored the project "Representation Theory of Finite Groups and Finite Di­ mensional Algebras". The proposal for this project was submitted by B. Huppert (Mainz), B. Fischer (Bielefeld), G. Michler (Essen), H. Pahlings (Aachen) and C. M. Ringel (Bielefeld) in order to strengthen the interaction between the different re­ search areas in representation theory. The Deutsche Forschungsgemeinschaft has given many research positions and fellowships for young algebraists enabling them to do research at their own uni­ versities or as visitors at well known research institutions in America, Australia, England and France. The whole project benefitted very much from an extensive exchange programme between German and American scientists sponsored by the Deutsche Forschungsgemeinschaft and by the National Science Foundation of the United States. This volume presents lectures given in a final conference and reports by members of the project. It is divided into two parts. The first part contains seven survey articles describing recent advances in different areas of representation theory. These articles do not only concentrate on the work done by the German research groups, but also inform on major developments of the subject at all. The volume omits those topics already treated in book form. In particular, it does not contain a survey on K.

Inhalt

1. Survey Articles:.- Clifford-Matrices.- Research in Representation Theory at Mainz (1984-1990).- Computational Aspects of Representation Theory.- Der Kenntnisstand in der konstruktiven Galoisschen Theorie.- Contributions to Modular Representation Theory of Finite Groups.- Recent Advances in the Representation Theory of Finite Dimensional Algebras.- The isomorphism problem for integral group rings of finite groups.- 2. Research Articles:.- Cohen-Macaulay and Gorenstein Artin Algebras.- Classical Invariants and the General Linear Group.- Partial characters of ?-separable groups.- First Cohomology Groups for Classical Lie Algebras.- Endotrivial modules and the Auslander-Reiten quiver.- Tame curve singularities with large conductor.- Polynomial representations of finite general linear groups in non-describing characteristic.- On Auslander-Reiten components for wild blocks.- On Gorenstein Algebras.- Decomposition numbers of finite groups of Lie type in non-defining characteristic.- Counting blocks of defect zero.- Group-theoretical descriptions of ring-theoretical invariants of group algebras.- Darstellungstheoretische Methoden bei der Realisierung einfacher Gruppen vom Lie Typ als Galoisgruppen.- Some new developments and open questions in the character theory of finite groups.- Some applications of representation theory.- A construction of orders of finite global dimensions.- Duality and forms in representation theory.