Fixed subgroups in Artin groups

We study fixed subgroups of automorphisms of any large-type Artin group \(A_{\Gamma}\). We define a natural subgroup \(\mathrm{Aut}_\Gamma(A_\Gamma)\) of \(\mathrm{Aut}(A_{\Gamma})\), and for every \(\gamma \in \mathrm{Aut}_\Gamma(A_\Gamma)\) we find the isomorphism type of \(\mathrm{Fix}(\gamma)\) and a generating set for a finite index subgroup. We show that \(\mathrm{Fix}(\gamma)\) is a finitely generated Artin group, with a uniform bound on the rank in terms of the number of vertices of \(\Gamma\). Finally, we provide a natural geometric characterisation of the subgroup \(\mathrm{Aut}_\Gamma(A_\Gamma)\), which informally is the maximal subgroup of \(\mathrm{Aut}(A_\Gamma)\) leaving the Deligne complex of \(A_{\Gamma}\) invariant.