Abstract

Let G be a simple classical algebraic group over an algebraically closed field

K of characteristic p ≥ 0 with natural module W . Let H be a closed subgroup of

G and let V be a nontrivial p-restricted irreducible tensor indecomposable rational

KG-module such that the restriction of V to H is irreducible. In this paper we

classify the triples (G, H, V ) of this form, where V = W, W

∗

and H is a disconnected

almost simple positive-dimensional closed subgroup of G acting irreducibly on W .

Moreover, by combining this result with earlier work, we complete the classification

of the irreducible triples (G, H, V ) where G is a simple algebraic group over K, and

H is a maximal closed subgroup of positive dimension.

Received by the editor November 27, 2012 and, in revised form, June 4, 2013.

Article electronically published on December 16, 2014.

DOI: http://dx.doi.org/10.1090/memo/1114

2010 Mathematics Subject Classification. Primary 20G05; Secondary 20E28, 20E32.

Key words and phrases. Classical algebraic group; disconnected maximal subgroup; irre-

ducible triple.

c 2014 American Mathematical Society

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