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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

On biunitary permutation matrices
and some subfactors of index 9


Authors: Uma Krishnan and V. S. Sunder
Journal: Trans. Amer. Math. Soc. 348 (1996), 4691-4736
MSC (1991): Primary 46L37
MathSciNet review: 1360226
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Abstract: This paper is devoted to a study of the subfactors arising from vertex models constructed out of `biunitary' matrices which happen to be permutation matrices. After a discussion on the computation of the higher relative commutants of the associated subfactor (in the members of the tower of Jones' basic construction), we discuss the principal graphs of these subfactors for small sizes $ N=k \leq 3 $ of the vertex model. Of the 18 possibly inequivalent such biunitary matrices when $ N = 3$, we compute the principal graphs completely in 15 cases, all of which turn out to be finite. In the last section, we prove that two of the three remaining cases lead to subfactors of infinite depth and discuss their principal graphs.


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Additional Information

Uma Krishnan
Affiliation: Stat-Math Unit, Indian Statistical Institute, R.V. College Post, Bangalore-560059, INDIA

V. S. Sunder
Affiliation: Stat-Math Unit, Indian Statistical Institute, R.V. College Post, Bangalore-560059, INDIA

DOI: http://dx.doi.org/10.1090/S0002-9947-96-01669-8
PII: S 0002-9947(96)01669-8
Received by editor(s): April 12, 1994
Additional Notes: The first author’s research was supported by the National Board for Higher Mathematics in India
Article copyright: © Copyright 1996 American Mathematical Society