  We prove a new automorphy lifting theorem for l-adic representations where we
impose a new condition at l, which we call `potential diagonalizability'. This
result allows for `change of weight' and seems to be substantially more
flexible than previous theorems along the same lines. We derive several
applications. For instance we show that any irreducible, odd, essentially
self-dual, regular, weakly compatible system of l-adic representations of the
absolute Galois group of a totally real field is potentially automorphic, and
hence is pure and its L-function has meromorphic continuation to the whole
complex plane and satisfies the expected functional equation.
