Group actions on graphs related to KrishnanSunder subfactors
Author:
Bina Bhattacharyya
Journal:
Trans. Amer. Math. Soc. 355 (2003), 433463
MSC (2000):
Primary 46L37
Published electronically:
October 8, 2002
MathSciNet review:
1932707
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Abstract: We describe the principal graphs of the subfactors studied by Krishnan and Sunder in terms of group actions on Cayleytype graphs. This leads to the construction of a tower of tree algebras, for every positive integer , which are symmetries of the KrishnanSunder subfactors of index . Using our theory, we prove that the principal graph of the irreducible infinite depth subfactor of index 9 constructed by Krishnan and Sunder is not a tree, contrary to their expectations. We also show that the principal graphs of the KrishnanSunder subfactors of index 4 are the affine A and D Coxeter graphs.
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 Gordon James and Adalbert Kerber, The representation theory of the symmetric group, Encyclopedia of Mathematics and its Applications, vol. 16, AddisonWesley Publishing Co., Reading, Mass., 1981, with a foreword by P. M. Cohn, with an introduction by Gilbert de B. Robinson. MR 83k:20003
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 Jonathan L. Gross and Thomas W. Tucker, Topological graph theory, John Wiley & Sons Inc., New York, 1987. MR 88h:05034
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 U. Haagerup and J. Schou, Some new subfactors of the hyperfinite subfactor, 1989, preprint.
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 V. F. R. Jones, Index for subfactors, Invent. Math. 72 (1983), 125. MR 84d:46097
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 V. F. R. Jones and V. S. Sunder, Introduction to subfactors, London Mathematical Society Lecture Note Series, vol. 234, Cambridge University Press, 1997. MR 98h:46067
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 U. Krishnan and V. S. Sunder, On biunitary permutation matrices and some subfactors of index , Trans. Amer. Math. Soc. 348 (1996), no. 12, 46914736. MR 97c:46077
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Additional Information
Bina Bhattacharyya
Affiliation:
Elance, 820A Kifer Rd., Sunnyvale, California 94086
Email:
Bina_Bhattacharyya_91@post.harvard.edu
DOI:
http://dx.doi.org/10.1090/S0002994702029860
PII:
S 00029947(02)029860
Received by editor(s):
March 8, 1999
Received by editor(s) in revised form:
December 17, 2001
Published electronically:
October 8, 2002
Article copyright:
© Copyright 2002
American Mathematical Society
