They are generated with a blessed erodeproof long sword and a non-cursed erodeproof large shield. There is a 1⁄20 chance that the sword will be converted into either Demonbane or Sunsword (if the chosen artifact does not exist yet), and a 1⁄4 chance the shield will instead be a shield of reflection.
In Dungeons & Dragons, an Aleax is an avatar of a deity, sent to punish a specific mortal. The Aleax takes on the target's exact appearance and carries identical equipment. For this reason, NetHack's Aleax imitates you when you #chat to it, and can be sent by a lawful god to punish those who transgress against them.
In UnNetHack, an Aleax behaves more like the D&D Aleax as described above, and will be generated wearing an erodeproof +0 copy of all of the player's equipment and weapons; artifacts will be converted to the base item.
An Aleax, according to the AD&D Fiend Folio, is a creature that
looks exactly like the character, and is sent by the character's
god to punish alignment violations. Obviously - and luckily - in
Nethack this is not the case.