Linear Representations of the Automorphism Group of a Free Group

Let F _n be the free group on n ≥ 2 elements and Aut(F _n ) its group of automorphisms. In this paper we present a rich collection of linear representations of Aut(F _n ) arising through the action of finite-index subgroups of it on relation modules of finite quotient groups of F _n . We show (under certain conditions) that the images of our representations are arithmetic groups. Received: November 2006, Accepted: March 2007