Low-dimensional linear representations of 𝐴𝑢𝑡𝐹_{𝑛},𝑛≥3

Abstract

We classify all complex representations of A u t F n , \mathrm {Aut} \: F_n, the automorphism group of the free group F n F_n ( n ≥ 3 ) , (n \geq 3), of dimension ≤ 2 n − 2. \leq 2n - 2. Among those representations is a new representation of dimension n + 1 n + 1 which does not vanish on the group of inner automorphisms.