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.
2010 Mathematics Subject Classification. Primary 20G05; Secondary 20E28, 20E32.
Key words and phrases. Classical algebraic group; disconnected maximal subgroup; irre-
c 2014 American Mathematical Society