Automorphisms of the affineSU(3) fusion rules

Ruelle, Philippe
(1994) Communications in Mathematical Physics — Vol. 160, n° 3, p. 475-492 (1994)

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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 (Z_2) is generated by the charge conjugation C. If k is not divisible by 3, the automorphism group (Z_2 x Z_2) is generated by C and the Altschuler--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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Ruelle, P. (1994). Automorphisms of the affineSU(3) fusion rules. Communications in Mathematical Physics, 160(3), 475-492. https://doi.org/10.1007/BF02173425 (Original work published 1994)