## On α-induction, chiral generators and modular invariants for subfactors (1999)

Venue: | Commun. Math. Phys |

Citations: | 38 - 10 self |

### BibTeX

@ARTICLE{Böckenhauer99onα-induction,,

author = {Jens Böckenhauer and David E. Evans and Yasuyuki Kawahigashi},

title = {On α-induction, chiral generators and modular invariants for subfactors},

journal = {Commun. Math. Phys},

year = {1999},

volume = {208},

pages = {429--487}

}

### OpenURL

### Abstract

We consider a type III subfactor N ⊂ M of finite index with a finite system of braided N-N morphisms which includes the irreducible constituents of the dual canonical endomorphism. We apply α-induction and, developing further some ideas of Ocneanu, we define chiral generators for the double triangle algebra. Using a new concept of intertwining braiding fusion relations, we show that the chiral generators can be naturally identified with the α-induced sectors. A matrix Z is defined and shown to commute with the S- and Tmatrices arising from the braiding. If the braiding is non-degenerate, then Z is a “modular invariant mass matrix ” in the usual sense of conformal field theory. We show that in that case the fusion rule algebra of the dual system of M-M morphisms is generated by the images of both kinds of α-induction, and that the structural information about its irreducible representations is encoded in the mass matrix Z. Our analysis sheds further light on the connection between (the classifications of) modular invariants and subfactors, and we will