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Group actions on graphs related to Krishnan-Sunder subfactors

Author: Bina Bhattacharyya
Journal: Trans. Amer. Math. Soc. 355 (2003), 433-463
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 Cayley-type graphs. This leads to the construction of a tower of tree algebras, for every positive integer $k$, which are symmetries of the Krishnan-Sunder subfactors of index $k^2$. 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 Krishnan-Sunder subfactors of index 4 are the affine A and D Coxeter graphs.

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Additional Information

Bina Bhattacharyya
Affiliation: Elance, 820A Kifer Rd., Sunnyvale, California 94086

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

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