THE IRREDUCIBLE SIX-DIMENSIONAL COMPLEX

REPRESENTATIONS OF Aut(F_{2}) THAT ARE NONTRIVIAL ON F_{2}

DRAGOMIR Ž. D – OKOVIĆ

Abstract. Denote by Φ_{2} the automorphism group of the free group F_{2} on two generators. We classify the irreducible 6-dimen-sional complex representations of Φ_{2} whose restriction to F_{2} is nontrivial. J. Dyer, E. Formanek, and E. Grossman have shown how the Bürau representation of the braid group B_{4} gives rise to a one-parameter family of irreducible 6-dimensional representations of Φ_{2}. The faithfulness question for these and some other closely related representations of Φ_{2} is open. Our classification shows that all other 6-dimensional representations of Φ_{2} are not faithful.