  The characters $\chi_\mu$ of nontwisted affine algebras at fixed level define
in a natural way a representation $R$ of the modular group $SL_2(Z)$. The
matrices in the image $R(SL_2(Z))$ are called the Kac-Peterson modular
matrices, and describe the modular behaviour of the characters. In this paper
we consider all levels of $(A_{r_1}\oplus\cdots\oplus A_{r_s})^{(1)}$, and for
each of these find all permutations of the highest weights which commute with
the corresponding Kac-Peterson matrices. This problem is equivalent to the
classification of automorphism invariants of conformal field theories, and its
solution, especially considering its simplicity, is a major step toward the
classification of all Wess-Zumino-Witten conformal field theories.
