Fusion rules on a parametrized series of graphs
Operator Algebras
2010-09-09 v2 Category Theory
Abstract
A series of pairs of graphs (Gamma_k, Gamma'_k), k = 0,1,2,... has been considered as candidates for dual pairs of principal graphs of subfactors of small Jones index above 4 and it has recently been proved that the pair (Gamma_k, Gamma'_k) comes from a subfactor if and only if k = 0 or k =1. We show that nevertheless there exists a unique fusion system compatible with this pair of graphs for all non-negative integers k.
Keywords
Cite
@article{arxiv.1008.5364,
title = {Fusion rules on a parametrized series of graphs},
author = {Marta Asaeda and Uffe Haagerup},
journal= {arXiv preprint arXiv:1008.5364},
year = {2010}
}
Comments
Typos corrected, smaller font used, 30pages