Palindromic automorphisms of right-angled Artin groups

Neil J. Fullarton and Anne Thomas

Abstract

We introduce the palindromic automorphism group and the palindromic Torelli group of a right-angled Artin group $A_{\mathrm{\Gamma }}$. The palindromic automorphism group $\mathrm{\Pi }{A}_{\mathrm{\Gamma }}$ is related to the principal congruence subgroups of $\mathrm{GL}(n,\mathbb{Z})$ and to the hyperelliptic mapping class group of an oriented surface, and sits inside the centraliser of a certain hyperelliptic involution in $\mathrm{Aut}(A_{\mathrm{\Gamma }})$. We obtain finite generating sets for $\mathrm{\Pi }{A}_{\mathrm{\Gamma }}$ and for this centraliser, and determine precisely when these two groups coincide. We also find generators for the palindromic Torelli group.