Modular invariants from subfactors: type I coupling matrices and intermediate subfactors

Böckenhauer, Jens and Evans, David Emrys 2000. Modular invariants from subfactors: type I coupling matrices and intermediate subfactors. Communications in Mathematical Physics 213 (2) , pp. 267-289. 10.1007/s002200000241

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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 ± 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 +≠Z −, and that Z need not be related to a type I invariant by such an automorphism

Item Type:	Article
Status:	Published
Schools:	Schools > Mathematics
Subjects:	Q Science > QA Mathematics
Publisher:	SpringerLink
ISSN:	0010-3616
Last Modified:	04 Jul 2024 08:44
URI:	https://orca.cardiff.ac.uk/id/eprint/12044

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