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The irreducible subfactor $(R^{S_3} \subset R)$, of index $6$, admits a principal graph with a multiplicity $2$ edge because the group $S_3$ admits an irreducible complex representation of dimension $2$.

The same for the subfactor $(R \subset M_2(R))$, of index $4$, but it is not irreducible.

Question: Is $6$ the smallest index for an irreducible subfactor to have a principal graph with an edge of multiplicity $>1$?

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  • $\begingroup$ You might consider adding a top-level- / arXiv tag to give this question more visibility. $\endgroup$
    – Stefan Kohl
    Oct 10, 2015 at 10:18

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