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Modular Invariants from Subfactors: Type I Coupling Matrices and Intermediate Subfactors

J. Böckenhauer·D. E. Evans
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Abstract

A braided subfactor determines a coupling matrix Z which commutes with the S- and T-matrices arising from the braiding. Such a coupling matrix is not necessarily of "type I", i.e. in general it does not have a block-diagonal structure which can be reinterpreted as the diagonal coupling matrix with respect to a suitable extension. We show that there are always two intermediate subfactors which correspond to left and right maximal extensions and which determine "parent" coupling matrices Z^\pm of type I. Moreover it is shown that if the intermediate subfactors coincide, so that Z^+=Z^-, then Z is related to Z^+ by an automorphism of the extended fusion rules. The intertwining relations of chiral branching coefficients between original and extended S- and T-matrices are also clarified. None of our results depends on non-degeneracy of the braiding, i.e. the S- and T-matrices need not be modular. Examples from SO(n) current algebra models illustrate that the parents can be different, Z^+\neq Z^-, and that Z need not be related to a type I invariant by such an automorphism.

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BibTeXRIS

J. Böckenhauer, D. E. Evans. 2000-02-17. Modular Invariants from Subfactors: Type I Coupling Matrices and Intermediate Subfactors. https://doi.org/10.1007/s002200000241

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