On the range of the index of subfactors (Q1908159)

Let \(L\subset N\) and \(N\subset M\) be inclusions of type \(\text{II}_1\) irreducible factors, with the same finite minimal index. The author shows that the value of the index is severely restricted if \(L\subset M\) contains a sector with index from the Jones series \(4\cos^2{\pi\over m}\). This result gives an interesting corollary which says that the minimal index of braided endomorphisms can only take four values in the interval (4,6).