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

University Of Oregon Eugene, Eugene OR

Investigators

Abstract

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.