Automorphisms of the affineSU(3) fusion rules

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 × Z 2 ) 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. * e-mail address: ruelle@stp.dias.ie 1. Introduction.

On the classification of diagonal coset modular invariants

“…The reasoning and calculations are very similar to that for n = 24. Here, put ρ ′′ = (11,11), ρ ′′′ = (19,19), and define m, m ′ , m ′′ , m ′′′ as before. Looking at s QED to Claim 7…”

“…In work done simultaneously but independently of [9], Ref. [19] classified the permutation invariants of SU (3) k (see eq. (2.2a) below); his argument is much longer than the one given in [9] but has the advantage of not requiring fusion rules, so it should generalize more easily to other SU (N ) k .…”

Symmetries of the Kac-Peterson modular matrices of affine algebras

“…Three special cases of the theorem were known previously: r = 1 [5], k = 1 [16], and r = 2 [10,24]. The remainder of this section is devoted to the proof of Theorem 1.…”