Palindromic automorphisms of right-angled Artin groups

Abstract

We introduce the palindromic automorphism group and the palindromic Torelli group of a right-angled Artin group $A_{\Gamma }$. The palindromic automorphism group $\Pi A_{\Gamma }$ is related to the principal congruence subgroups of 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 Aut$(A_{\Gamma })$. We obtain finite generating sets for $\Pi A_{\Gamma }$ and for this centraliser, and determine precisely when these two groups coincide. We also find generators for the palindromic Torelli group.