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 \(A_\Gamma\). The palindromic automorphism group \(\Pi A_\Gamma\) 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 \(\mathrm{Aut}(A_\Gamma)\). 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.