The irreducible six-dimensional complex representations of Aut(F-2) that are nontrivial on F-2

Denote by Phi (2) the automorphism group of the free group F-2 On two gener ators. We classify the irreducible 6-dimensional complex representations of Phi (2) whose restriction to F-2 is nontrivial. J. Dyer, E. Formanek, and E. Grossman have shown how the Burau representation of the braid group B-4 gives rise to a one-parameter family of irreducible 6-dimensional represent ations of Phi (2). The faithfulness question for these and some other close ly related representations of Phi (2) is open. Our classification shows tha t all other 6-dimensional representations of Phi (2) are not faithful.