That's totally fixable as long as there are no other cross grain cracks. I have used TBIII and super glue to repair split cedar shafts and by adding a wrap or 2 at your fletching its good to go. The arrow might have a little more spine weight but with the split being only in the rear, probably not much.
For the nock, Grind a long, flat taper in the nock end of the shaft removing the damaged area. Grind the same bevel in a cedar cut off and glue and wrap until the glue is set. Then cut to length and cut your nock in again. On the one I repaired it had a raw hide spine so I had to add that too. Yours looks like you have a spine in it also.
You may have to remove the feathers yo do the repair . After the repair is done re-fletch and add a wrap around where the splice is just for security. Pat
