✦ LIBER ✦

On the Range of the Index of Subfactors

✍ Scribed by K.H. Rehren

Publisher: Elsevier Science
Year: 1995
Tongue: English
Weight: 416 KB
Volume: 134
Category: Article
ISSN: 0022-1236
DOI: 10.1006/jfan.1995.1141

No coin nor oath required. For personal study only.

✦ Synopsis

A simple numerical argument is given that the minimal (Jones) index of a subfactor (N \subset M) is strongly restricted if for (L \subset N) with the same index, the subfactor (L \subset M) contains a sector with index from the Jones series (4 \cos ^{2} \pi / m). E.g.. (N \subset M) might be the Jones extension of, or isomorphic with, (L \subset N). As a corollary extending results of Longo, the range of the index of braided endomorphisms is completely computed up to the value (I n d=6). An algebraic version of the argument is outlined and is expected to generalize to braided endomorphisms the square of which contains a sector with index from the Hecke or Birman-Wenzl-Murakami series. This would allow to push the determination of the range of the index beyond 6. ' 1995 Academic Press. Inc.

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