English

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

R2 v1 2026-06-21T16:07:36.163Z