Specialists have at-will use of cantrips, in combat this counts as your round.
A specialist has a +1 to saving throws he makes against his specialized school, and enemies have a -1 to the saving throws against spells of his school. This is per level of experience, so a +10 and -10 at level 10, a +20 and -20 at 20.
In addition to this, a specialist is banned from using spells in his ‘opposition school’.
Specialists receive a bonus of +15% when learning spells from their school and a penalty of -15% when learning spells from other schools. The bonus or penalty is applied to the percentile dice roll the player must make when the character tries to learn a new spell.
Whenever a specialist reaches a new spell level, he automatically gains one spell of his school to add to his spell books. This spell can be selected by the DM or he can allow the player to pick. No roll for learning the spell need be made. It is assumed that the character has discovered this new spell during the course of his research and study.
When a specialist wizard attempts to create a new spell (using the rules given in the DMG), the DM should count the new spell as one level less (for determining the difficulty) if the spell falls within the school of the specialist. An enchanter attempting to create a new enchantment spell would have an easier time of it than an illusionist attempting to do the same.
P.S. Some specializations (like Geometer) work with that same basis but have more specifics to be put in about it, as per the DM’s ruling on the matter. When the specialization pages are finished this information will be decided and added.
P.S.S This information isn’t set in stone as the DM may decide to change it. It is merely what the PHB says on the matter, before specifically saying ‘the DM can decide that some of these dont work as they do, usually with a con and a pro to the specialist.’
P.S.S.S I copied this from the other campaign I’m in and while I havn’t had time to edit this information it is assumed that anything here is correct within the campaign, and if it isn’t then I will change it as we play on a more case-by-case basis.