# Exotic Subfactors of Finite Depth with Jones Indices and

@article{Asaeda1998ExoticSO, title={Exotic Subfactors of Finite Depth with Jones Indices and}, author={Marta M. Asaeda and Uffe Haagerup}, journal={Communications in Mathematical Physics}, year={1998}, volume={202}, pages={1-63} }

Abstract:We prove existence of subfactors of finite depth of the hyperfinite II1 factor with indices and . The existence of the former was announced by the second named author in 1993 and that of the latter has been conjectured since then. These are the only known subfactors with finite depth which do not arise from classical groups, quantum groups or rational conformal field theory.

## 32 Citations

### Subfactors of index exactly 5

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We give the classification of subfactor planar algebras at index exactly 5. All the examples arise as standard invariants of subgroup subfactors. Some of the requisite uniqueness results come from…

### Subfactors of index less than 5, part 2: quadratic tangles and triple points

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This paper gives two applications of Jones’s quadratic tangles techniques to the classification of subfactors with index below 5. In particular, we eliminate two of the five families of possible…

### On the Jones Index Values for Conformal Subnets

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We consider the smallest values taken by the Jones index for an inclusion of local conformal nets of von Neumann algebras on S1 and show that these values are quite more restricted than for an…

### An obstruction to subfactor principal graphs from the graph planar algebra embedding theorem

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We find a new obstruction to the principal graphs of subfactors. It shows that in a certain family of 3‐supertransitive principal graphs, there must be a cycle by depth 6, with one exception, the…

### On Ocneanu's theory of double triangle algebras for subfactors and classification of irreducible connections on the Dynkin diagrams

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### On Haagerup’s List of Potential Principal Graphs of Subfactors

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We show that any graph, in the sequence given by Haagerup in 1991 as that of candidates of principal graphs of subfactors, is not realized as a principal graph except for the smallest two. This…

### QUANTUM GALOIS CORRESPONDENCE FOR SUBFACTORS

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- 1999

Ocneanu has obtained a certain type of quantized Galois correspondence for the Jones subfactors of type An and his arguments are quite general. By making use of them in a more general context, we…