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.