Fusion rules on a parametrized series of graphs

Details Fusion rules on a parametrized series of graphs Fusion rules on a parametrized series of graphs

2010-08-31

arxiv.org/abs/1008.5364v2

Mathematics

Operator Algebras

Typos corrected, smaller font used, 30pages

Scientific paper

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.

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