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

Potapchik, A.; Rapinchuk, A.

doi:10.1090/S0002-9947-99-02293-X

Low-dimensional linear representations of $\operatorname {Aut} F_n, n \geq 3$
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Trans. Amer. Math. Soc. 352 (2000), 1437-1451 Request permission

Abstract:

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

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