On irreducible subgroups of simple algebraic groups

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.


Published in:
Mathematische Annalen, 367, 3-4, 1259-1309
Year:
2017
Publisher:
Heidelberg, Springer Heidelberg
ISSN:
0025-5831
Laboratories:




 Record created 2017-05-01, last modified 2018-03-17


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