Low-dimensional representations of \(\text{Aut}(F_ 2)\)
Let \(F_2\) be the free group of rank two and \(\Phi_2\) its automorphism group. The authors consider indecomposable representations \(\rho\) of \(\Phi_2\) of degree \(n\leq 4\), over an algebraically closed field \(K\), such that \(\rho(F_2)\neq 1\). They show that there are no such representations if \(n\leq 2\). If \(\rho(F)\) is infinite then, up to weak equivalence, there exist for \(n=3\) only one such representation, and for \(n=4\) two if \(\text{char }K\neq2,3\), one if \(\text{char }K=3\), and none if \(\text{char }K=2\). All the representations mentioned above are reducible and listed explicitly.
scientific article; zbMATH DE number 885530