1994/08/22 by Terry Gannon, Gannon, Terry · 1 citation
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #hep-th
paper · pdf · doi:10.48550/arxiv.hep-th/9408119
8 pp. (plain tex)
arxiv created 1994/08/22 · arxiv updated 2009/11/30
In this paper we find all permutations of the level k weights of the affine algebra Ar(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 Ar,k(1) automorphism invariants were known only for r=1,2 ∀ k, and k=1 ∀ r. This is a major step toward the full classification of all Ar,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 Ar,k(1) fusion ring.