Automorphisms of the affine SU(3) fusion rules

Details Automorphisms of the affine SU(3) fusion rules Automorphisms of the affine SU(3) fusion rules

1993-01-29

arxiv.org/abs/hep-th/9301127v1

Commun.Math.Phys.160:475-492,1994

Physics

High Energy Physics

High Energy Physics - Theory

21 pages, plain TeX, DIAS-STP-92-45

Scientific paper

10.1007/BF02173425

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 Altsch\"uler--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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