A note on virtual duality and automorphism groups of right-angled Artin
groups

A theorem of Brady and Meier states that a right-angled Artin group is a
duality group if and only if the flag complex of the defining graph is
Cohen--Macaulay. We use this to give an example of a RAAG with the property
that its outer automorphism group is not a virtual duality group. This gives a
partial answer to a question of Vogtmann. In an appendix, Br\"uck describes how
he used a computer-assisted search to find further examples.