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

最近的一份文件的提议者获得了新的结果，幂幺类，子群的A1型，饱和。 建议利用这些结果得到例外代数群中的张量积定理，从而阐明代数群在特征0和特征p上的子群结构之间的关系。 此外，提案人打算完成长期的项目，确定最大的子群简单的代数群，扩大现有的成果，提升有限群代数群，并获得额外的成果非通用子群的例外groups.Lie理论是一个主题的根本重要性，在数学以及各种硬科学。 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，进一步的见解总是有价值的。 该提案旨在将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.