Almost irreducible tensor squares

Let G be a covering group of a finite almost simple group. We determine those faithful irreducible complex characters #chi# of G for which #chi# x #chi#*-1 is again irreducible. This gives a classification of the quasi-simple absolutely irreducible subgroups of GL_n(q) or order prime to q which act irreducibly on the Lie algebra of type A_n_-_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 SU_n(F_2) and Sp_2_n(F_3). (orig.)Available from TIB Hannover: RR 1606(96-54) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman