[RPG] Sword of Sharpness Critical Hit Resolution

Yes, the extra damage is maximized on a crit.

From the Players Handbook FAQ:

1. Which dice do I maximize when scoring a critical hit?

Only the dice you would normally roll to calculate damage are maximized. If another bonus (like from a weapon or feat) causes you to roll extra damage dice when scoring a critical hit, those dice are rolled as normal.

And from consensus on the WotC forums:

Which dice do you max on a critical hit? If a bonus (like from a weapon or feat) causes you to roll extra damage dice when scoring a critical hit, those dice are not maxed. Other dice like hunter's quarry, sneak attack, warlock's curse, etc. are all maxed. Discussed here and in the 4e PHB FAQ.

I see no reason that a power that triggers on a hit is any different from anything else like a class feature such as Sneak Attack or the free action granted by the Hunter's Quarry power.

As summarized by jprete:

The procedure here is something like the following: figure out what the damage roll would be without a critical hit, considering all effects; maximize that; and then go ahead and add bonus effects that only trigger on a crit, without maximizing them

Your critical hits are not affected at all!

If you roll a 20 on an attack roll, meaning the die itself shows a 20, it is always a critical hit, as explained on PHB p. 194:

If the d20 roll for an attack is a 20, the attack hits regardless of any modifiers or the target's AC. This is called a critical hit, [...]

The GWM damage bonus is also not affected, because only the damage dice are doubled. You can still add your brutal critical bonus dice, but the +10 on damage does not change, because it is not a die.