ON SOME SUBFACTORS OF INTEGER INDEX ARISING FROM VERTEX MODELS

This paper is devoted to the study of subfactors arising out of commut ing squares constructed out of the simplest possible vertex models. Af ter setting up the necessary general background, we start with two cla sses of commuting squares and compute the principal graphs of the resu lting subfactors, one of them being related to the group dual of a sui table (closed) subgroup of U(N), and the other to the Cayley graph of a (non-closed) group, module scalars, generated by N elements of U(N). In the last section, we ''classify'' the commuting squares in dimensi on 2, and identify the possible resulting principal graphs as A((2n-1) )((1)), 1 less than or equal to n less than or equal to infinity. (C) 1996 Academic Press, Inc.