Automorphisms of the affine SU(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 x 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.

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

References in corpus (2)

• su(3)k fusion coefficients
• Implications of an arithmetical symmetry of the commutant for modular invariants

Cited by in corpus (4)

• Automorphism Modular Invariants of Current Algebras
• The Classification of SU(3) Modular Invariants Revisited
• Implications of an arithmetical symmetry of the commutant for modular invariants
• Symmetries of the Kac-Peterson Modular Matrices of Affine Algebras