457 research outputs found
Irreducible subgroups of simple algebraic groups - a survey
Let be a simple linear algebraic group over an algebraically closed field
of characteristic , let be a proper closed subgroup of
and let be a nontrivial finite dimensional irreducible rational
-module. We say that is an irreducible triple if is
irreducible as a -module. Determining these triples is a fundamental
problem in the representation theory of algebraic groups, which arises
naturally in the study of the subgroup structure of classical groups. In the
1980s, Seitz and Testerman extended earlier work of Dynkin on connected
subgroups in characteristic zero to all algebraically closed fields. In this
article we will survey recent advances towards a classification of irreducible
triples for all positive dimensional subgroups of simple algebraic groups.Comment: 31 pages; to appear in the Proceedings of Groups St Andrews 201
- …