Implications of an arithmetical symmetry of the commutant for modular invariants

1992/12/08 by Ph. Ruelle, Ph Ruelle, E. Thiran +3 · 4 citations
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #hep-th

paper · pdf · doi:10.1016/0550-3213(93)90125-9

published as Nucl.Phys.B402:693-708,1993 · 17 pages, plain TeX, DIAS-STP-92-26

arxiv created 1992/12/08 · openalex publication_date 1993/08/01 · arxiv updated 2010/11/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We point out the existence of an arithmetical symmetry for the commutant of the modular matrices S and T. This symmetry holds for all affine simple Lie algebras at all levels and implies the equality of certain coefficients in any modular invariant. Particularizing to SU(3)_k, we classify the modular invariant partition functions when k+3 is an integer coprime with 6 and when it is a power of either 2 or 3. Our results imply that no detailed knowledge of the commutant is needed to undertake a classification of all modular invariants.

Citations

• Automorphisms of the affineSU(3) fusion rules

Cited by

• Automorphisms of the affineSU(3) fusion rules
• Comments on the links between su(3) modular invariants, simple factors in the Jacobian of Fermat curves, and rational triangular billiards
• On the classification of diagonal coset modular invariants
• The rank-four heterotic modular invariant partition functions