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Generalized Longo-Rehren subfactors and alpha-induction

Yasuyuki Kawahigashi
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Abstract

We study the recent construction of subfactors by Rehren which generalizes the Longo-Rehren subfactors. We prove that if we apply this construction to a non-degenerately braided subfactor N subset M and alpha-induction, then the resulting subfactor is dual to the Longo-Rehren subfactor M tensor M^opp subset R arising from the entire system of irreducible endomorphisms of M resulting from alpha-induction. As a corollary, we solve a problem on existence of braiding raised by Rehren negatively. Furthermore, we generalize our previous study with Longo and Muger on multi-interval subfactors arising from a completely rational conformal net of factors on S^1 to a net of subfactors and show that the (generalized) Longo-Rehren subfactors and alpha-induction naturally appear in this context.

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Yasuyuki Kawahigashi. 2001-07-18. Generalized Longo-Rehren subfactors and alpha-induction. https://doi.org/10.1007/s002200200608

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