scholarly journals Positivity and periodicity of Q-systems in the WZW fusion ring

2017 ◽  
Vol 311 ◽  
pp. 532-568 ◽  
Author(s):  
Chul-hee Lee
Keyword(s):  
Fusion Ring

scholarly journals The center of the extended Haagerup subfactor has 22 simple objects

2017 ◽  
Vol 28 (01) ◽  
pp. 1750009 ◽  
Author(s):  
Scott Morrison ◽  
Kevin Walker
Keyword(s):  
Fusion Category ◽  
Dimension Function ◽  
Fusion Ring ◽  
Fusion Categories ◽  
Modular Data ◽  
Grothendieck Rings ◽  
Combinatorial Data

We explain a technique for discovering the number of simple objects in [Formula: see text], the center of a fusion category [Formula: see text], as well as the combinatorial data of the induction and restriction functors at the level of Grothendieck rings. The only input is the fusion ring [Formula: see text] and the dimension function [Formula: see text]. In particular, we apply this to deduce that the center of the extended Haagerup subfactor has 22 simple objects, along with their decompositions as objects in either of the fusion categories associated to the subfactor. This information has been used subsequently in [T. Gannon and S. Morrison, Modular data for the extended Haagerup subfactor (2016), arXiv:1606.07165 .] to compute the full modular data. This is the published version of arXiv:1404.3955 .

A Ring-Fusion/Ring-Fission Mechanism for the Metathesis Reaction of Macrocyclic Formaldehyde Acetals

2006 ◽  
Vol 12 (33) ◽  
pp. 8566-8570 ◽  
Author(s):  
Roberta Cacciapaglia ◽  
Stefano Di Stefano ◽  
Luigi Mandolini
Keyword(s):  
Metathesis Reaction ◽  
Ring Fusion ◽  
Fusion Ring ◽  
Ring Fission

scholarly journals Generalized orbifold construction for conformal nets

2017 ◽  
Vol 29 (01) ◽  
pp. 1750002 ◽  
Author(s):  
Marcel Bischoff
Keyword(s):  
Fixed Point ◽  
Finite Index ◽  
Fusion Category ◽  
Proper Action ◽  
Completely Positive ◽  
Double Cosets ◽  
Fusion Ring ◽  
Galois Correspondence ◽  
A Finite Group ◽  
Orbifold Construction

Let [Formula: see text] be a conformal net. We give the notion of a proper action of a finite hypergroup [Formula: see text] acting by vacuum preserving unital completely positive (so-called stochastic) maps on [Formula: see text] which generalizes the proper action of a finite group [Formula: see text]. Taking the fixed point under such an action gives a finite index subnet [Formula: see text] of [Formula: see text], which generalizes the [Formula: see text]-orbifold net. Conversely, we show that if [Formula: see text] is a finite inclusion of conformal nets, then [Formula: see text] is a generalized orbifold [Formula: see text] of the conformal net [Formula: see text] by a unique finite hypergroup [Formula: see text]. There is a Galois correspondence between intermediate nets [Formula: see text] and subhypergroups [Formula: see text] given by [Formula: see text]. In this case, the fixed point of [Formula: see text] is the generalized orbifold by the hypergroup of double cosets [Formula: see text]. If [Formula: see text] is a finite index inclusion of completely rational nets, we show that the inclusion [Formula: see text] is conjugate to an intermediate subfactor of a Longo–Rehren inclusion. This implies that if [Formula: see text] is a holomorphic net, and [Formula: see text] acts properly on [Formula: see text], then there is a unitary fusion category [Formula: see text] which is a categorification of [Formula: see text] and [Formula: see text] is braided equivalent to the Drinfel’d center [Formula: see text]. More generally, if [Formula: see text] is a completely rational conformal net and [Formula: see text] acts properly on [Formula: see text], then there is a unitary fusion category [Formula: see text] extending [Formula: see text], such that [Formula: see text] is given by the double cosets of the fusion ring of [Formula: see text] by the Verlinde fusion ring of [Formula: see text] and [Formula: see text] is braided equivalent to the Müger centralizer of [Formula: see text] in the Drinfel’d center [Formula: see text].

Irreducible ℤ+-modules of near-group fusion ring K(ℤ3, 3)

2018 ◽  
Vol 13 (4) ◽  
pp. 947-966
Author(s):  
Chengtao Yuan ◽  
Ruju Zhao ◽  
Libin Li
Keyword(s):  
Fusion Ring ◽  
Group Fusion

scholarly journals Zero Modes’ Fusion Ring and Braid Group Representations for the Extended Chiral su(2) WZNW Model

2007 ◽  
Vol 82 (2-3) ◽  
pp. 117-151 ◽  
Author(s):  
Paolo Furlan ◽  
Ludmil Hadjiivanov ◽  
Ivan Todorov
Keyword(s):  
Braid Group ◽  
Group Representations ◽  
Fusion Ring ◽  
Zero Modes ◽  
Wznw Model

scholarly journals Cardy states as idempotents of fusion ring in string field theory

2004 ◽  
Vol 590 (3-4) ◽  
pp. 303-308 ◽  
Author(s):  
Isao Kishimoto ◽  
Yutaka Matsuo
Keyword(s):  
Field Theory ◽  
String Field Theory ◽  
Fusion Ring
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