THE COMPLEX INDECOMPOSABLE REPRESENTATIONS OF Aut(F2) OF DEGREE LESS THAN SIX

Abstract

Denote by Φ2 the automorphism group of the free group on two generators. We classify the indecomposable complex linear representations of Φ2 of degree at most 5, and determine which ones have an infinite image. As a side-effect, our classification incorporates all the indecomposable representations of GL2(Z) in these degrees.