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Implications of an arithmetical symmetry of the commutant for modular invariants

Ph Ruelle·E Thiran·J Weyers
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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.

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Ph Ruelle, E Thiran, J Weyers. 1992-12-08. Implications of an arithmetical symmetry of the commutant for modular invariants. https://doi.org/10.1016/0550-3213(93)90125-9

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