U. Krishnan et Vs. Sunder, ON BIUNITARY PERMUTATION MATRICES AND SOME SUBFACTORS OF INDEX-9, Transactions of the American Mathematical Society, 348(12), 1996, pp. 4691-4736
This paper is devoted to a study of the subfactors arising from vertex
models constructed out of 'biunitary' matrices which happen to be per
mutation matrices. After a discussion on the computation of the higher
relative commutants of the associated subfactor (in the members of th
e tower of Jones' basic construction), we discuss the principal graphs
of these subfactors for small sizes (N = k less than or equal to 3) o
f the vertex model. Of the 18 possibly inequivalent such biunitary mat
rices when N = 3, we compute the principal graphs completely in 15 cas
es, 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 d
epth and discuss their principal graphs.