On irreducible subgroups of simple algebraic groups

2014/12/09 by Burness, Timothy C., Marion, Claude, Testerman, Donna M.
#FOS: Mathematics #Group Theory (math.GR) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1412.3130

Abstract

Let G be a simple algebraic group over an algebraically closed field K of characteristic p\geqslant 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.

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