The Classification of SU(m)_{k} Automorphism Invariants

Details The Classification of SU(m)_{k} Automorphism Invariants The Classification of SU(m)_{k} Automorphism Invariants

1994-08-22

arxiv.org/abs/hep-th/9408119v1

Physics

High Energy Physics

High Energy Physics - Theory

8 pp. (plain tex)

Scientific paper

In this paper we find all permutations of the level k weights of the affine algebra A_r^{(1)} which commute with both its S and T modular matrices. We find that all of these are simple current automorphisms and their conjugations. Previously, the A_{r,k}^{(1)} automorphism invariants were known only for r=1,2 \forall k, and k=1 \forall r. This is a major step toward the full classification of all A_{r,k}^{(1)} modular invariants; the simplicity of this proof strongly suggests that the full classification should be accomplishable. In an appendix we collect some new results concerning the A_{r,k}^{(1)} fusion ring.

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