Group actions on graphs related to Krishnan-Sunder subfactors

Bhattacharyya, Bina

doi:10.1090/S0002-9947-02-02986-0

Group actions on graphs related to Krishnan-Sunder subfactors
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Trans. Amer. Math. Soc. 355 (2003), 433-463 Request permission

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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