  In this paper we find all permutations of the level k weights of the affine
algebra A_r^{(1)} which commute with both its S and T modular matrices. We find
that all of these are simple current automorphisms and their conjugations.
Previously, the A_{r,k}^{(1)} automorphism invariants were known only for r=1,2
\forall k, and k=1 \forall r. This is a major step toward the full
classification of all A_{r,k}^{(1)} modular invariants; the simplicity of this
proof strongly suggests that the full classification should be accomplishable.
In an appendix we collect some new results concerning the A_{r,k}^{(1)} fusion
ring.
