Galois groups and an obstruction to principal graphs of subfactors

Details Galois groups and an obstruction to principal graphs of subfactors Galois groups and an obstruction to principal graphs of subfactors

2006-05-12

arxiv.org/abs/math/0605318v3

Mathematics

Operator Algebras

12 pages. Typos corrected, reference added. To appear in International Journal of Mathematics

Scientific paper

The Galois group of the minimal polymonal of a Jones index value gives a new type of obstruction to a principal graph, thanks to a recent result of P.Etingof, D.Nikshych, and V.Ostrik. We show that the sequence of the graphs given by Haagerup as candidates of principal graphs of subfactors, are not realized as principal graphs for 77, and give an evidence using Mathematica for smaller graphs among them for n>55. The problem for the case n=7 remains open, however, it is highly likely that it would be realized as a principal graph, thanks to numerical computation by Ikeda.

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