New Ideas In the Representation Theory of Finite Groups

Alperin 9619727首席研究员将继续发展他的方法来研究摄动模的结构，特别是着眼于Dade群的阶的问题和从特征p提升的问题。他将与Linckelmann和Rouquier一起，继续他们的工作，将Puig的整个方法建立在模论的基础上。他将与G.Mason合作，将模的复杂性理论应用于李型群。我们将发展团的概念，推广块的概念，并将同伦理论中的一些结果放入一个代数概念中加以推广。群论的领域是对称性的数学理论，与数学、编码论、数论和几何等学科之外的许多其他学科相互作用。ıS特别研究的领域是有限群和表示论，它是群论和线性代数之间的交界点。这是一个有百年历史的课题，但仍然面临着许多悬而未决的问题，有许多突破的机会。

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.