The character begins as a 10th level human fighter and then received an extra benefit at the adventure's ending; he is discovered to be an Elan (not a human, GM's alchemy) gaining psionic capacities. For the next two levels, he advanced as an Aegis becoming a multi-class fighter 10/aegis 2.
In the manual is:
Greater Weapon Specialization (Combat)
Choose one type of weapon (including unarmed strike or grapple) for which you possess the Weapon Specialization feat. Your attacks with the chosen weapon are more devastating than normal.
Prerequisites: Proficiency with selected weapon, Greater Weapon Focus with selected weapon, Weapon Focus with selected weapon, Weapon Specialization with selected weapon, 12th-level fighter.
Can this character take "Greater Weapon Specialization"?