LetGbe a covering group of a finite almost simple group. We determine those faithful irreducible complex charactersxofGfor whichx⊗x*- 1 is again irreducible. This gives a classification of the quasi-simple absolutely irreducible subgroups ofGLn(q) of order prime toqwhich act irreducibly on the Lie algebra of typeAn-1 via the adjoint representation. The proof uses Lusztig’s description of the degrees of irreducible characters of reductive groups and the determination of Brauer trees by Fong and Srinivasan to handle the case of groups of Lie type. It turns out that the only infinite series of examples are characters of Weyl representations for SUn(Fn) and Sp2n(F3).