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\geq 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 the authors classify the triples (G,H,V) of this form, where V \neq 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, they complete the classification of the irred