Fixed subgroups in Artin groups

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