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

最近，作者的一篇论文得到了关于幂等类、A1型子群和饱和度的新结果。利用这些结果得到了例外代数群的张量积定理，从而阐明了特征为0的代数群的子群结构与特征p之间的关系，并进一步得到了关于饱和度的结果。此外，作者还打算完成关于确定单代数群的极大子群的长期项目，将已有的关于提升有限群的结果推广到代数群，并得到关于例外群的非一般子群的更多结果。Lie理论在数学和各种硬科学中都是一个基本的重要课题。李理论中的主要对象(李代数、李群、代数群、李型有限群)在数学中无处不在，进一步的洞察总是有价值的。该提案旨在将这一理论的各个方面联系起来，并在一些最困难的领域取得重要的新成果。

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.