Burness, Timothy C.
Marion, Claude
Testerman, Donna M.
On irreducible subgroups of simple algebraic groups
Mathematische Annalen
Mathematische Annalen
Mathematische Annalen
Mathematische Annalen
51
367
3-4
2017
2017
Let G be a simple algebraic group over an algebraically closed field K of characteristic p >= 0, let H be a proper closed subgroup of G and let V be a nontrivial irreducible KG-module, which is p-restricted, tensor indecomposable and rational. Assume that the restriction of V to H is irreducible. In this paper, we study the triples (G, H, V) of this form when G is a classical group and H is positive-dimensional. Combined with earlier work of Dynkin, Seitz, Testerman and others, our main theorem reduces the problem of classifying the triples (G, H, V) to the case where G is an orthogonal group, V is a spin module and H normalizes an orthogonal decomposition of the natural KG-module.
Springer Heidelberg
0025-5831
Mathematische Annalen
Journal Articles
10.1007/s00208-016-1432-z