Linear representations of the automorphism group of a free group
by
Alex Lubotzky
Hebrew University of Jerusalem

Let F be a free group on n>2 generators. The group A=Aut(F) is a much studied group but very little seems to be known on its (finite dimensional) linear representations. We present a very rich collection of new representations which show that the representation theory of Aut(F) is much richer than assumed before. By studying the action of suitable finite index subgroups of A of the relation module of carefully chosen finite groups we show that many interesting arithmetic groups appear as images of representations of A. Joint work with Fritz Grunewald.

Date received: February 22, 2006