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Let $G$ be a simple classical algebraic group over an algebraically closed field $K$ of characteristic $pgeq 0$ 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 $V
eq W,W^{*}$ 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...