New Ideas In the Representation Theory of Finite Groups

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Alperin 9619727 The principal investigator will continue to develop his approach to the structure of endo-permuation modules, especially with a view to the question of the rank of the Dade group and the question of lifting from characteristic p. He, together with Linckelmann and Rouquier, will proceed with their work on putting the whole approach of Puig on a module-theoretic basis. Jointly with G. Mason, he will apply the complexity theory of modules to Lie type groups. The idea of a clique, generalizing the concept of a block, will be developed and some results from homotopy theory will be put in an algebraic concept and generalized. The field of group theory is the mathematical theory of symmetry and interacts with many other disciplines,for example physics and chemistry outside of mathematics, coding theory, number theory and geometry inside mathematics.The investigatorıs particular area is finite groups and representation theory which is the interface between group theory and linear algebra. It is a hundred year old subject but still facing great unsolved problems and with many opportunities for breakthroughs.