  Let $W$ be a vector space over an algebraically closed field $k$. Let $H$ be
a quasisimple group of Lie type of characteristic $p\ne {\rm char}(k)$ acting
irreducibly on $W$. Suppose also that $G$ is a classical group with natural
module $W$, chosen minimally with respect to containing the image of $H$ under
the associated representation. We consider the question of when $H$ can act
irreducibly on a $G$-constituent of $W^{\otimes e}$ and study its relationship
to the maximal subgroup problem for finite classical groups.
