Automorphisms of the affine SU(3) fusion rules
Philippe Ruelle
Abstract
We classify the automorphisms of the (chiral) level-k affine SU(3) fusion rules, for any value of k, by looking for all permutations that commute with the modular matrices S and T. This can be done by using the arithmetic of the cyclotomic extensions where the problem is naturally posed. When k is divisible by 3, the automorphism group (Z2) is generated by the charge conjugation C. If k is not divisible by 3, the automorphism group (Z2 x Z2) is generated by C and the Altschüler--Lacki--Zaugg automorphism. Although the combinatorial analysis can become more involved, the techniques used here for SU(3) can be applied to other algebras.
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