Structure and Representations of Algebraic Groups and Finite Groups of Lie Type

作者在最近的一篇论文中得到了关于A1型的单能类、子群和饱和的新结果。利用这些结果得到了例外代数群中的张量积定理，阐明了特征0和特征p上代数群的子群结构之间的关系，并给出了关于饱和的进一步结果。此外，拟完成长期存在的简单代数群的极大子群的确定课题，将有限群提升的现有结果推广到代数群，并获得例外群的非一般子群的附加结果。李论在数学和各种硬科学中都是一个重要的基础学科。李论的主要对象（李代数、李群、代数群、李型有限群）在数学中无处不在，深入了解总是有价值的。该建议旨在将理论的各个方面联系起来，并在一些最困难的领域获得重要的新结果。

A recent paper of the proposer obtains new results on unipotent classes, subgroups of type A1, and saturation. It is proposed to use these results to obtain tensor product theorems in exceptional algebraic groups, which would clarify the relationship between the subgroup structure of algebraic groups in characteristic 0 and characteristic p. Further results on saturation are also proposed. In addition the proposer intends to complete the long standing project on determining the maximal subgroups of simple algebraic groups, to extend existing results on lifting finite groups to algebraic groups, and to obtain additional results on nongeneric subgroups of exceptional groups.Lie theory is a subject of fundamental importance in mathematics as well as in various of the hard sciences. The main objects in Lie theory (Lie algebras, Lie groups, algebraic groups, finite groups of Lie type) are pervasive across mathematics and further insight is always valuable. The proposal is aimed at connecting various aspects of the theory and to obtain important new results in some of the most difficult areas.