Irreducible almost simple subgroups of classical algebraic groups

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.