AUTOMORPHISMS OF THE AFFINE SU(3) FUSION RULES

We classify the automorphisms of the (chiral) level-k affine SU (3) fu sion rules, for any value of k, by looking for all permutations that c ommute with the modular matrices S and T. This can be done by using th e arithmetic of the cyclotomic extensions where the problem is natural ly posed. When k is divisible by 3, the automorphism group (approximat ely Z2) is generated by the charge conjugation C. If k is not divisibl e by 3, the automorphism group (approximately Z2 X Z2) is generated by C and the Altschuler-Lacki-Zaugg automorphism. Although the combinato rial analysis can become more involved, the techniques used here for S U (3) can be applied to other algebras.