By generalizing constructions
in Kosaki (1994) and Kosaki and Longo, we will construct an AFD type
III0 factor with uncountably many non-conjugate subfactors such that (i)
each subfactor has the same flow of weights as the ambient factor, and (ii)
the principal and the dual principal graphs are of a specific form. We will
deal with two cases: (a) the graphs are described by the Dynkin diagram
A4m−3, and (b) the graphs are the ones given by a pair of a group and its
subgroup (see Kosaki and Yamagami) which are simultaneous semi-direct
products. Subfactors are distinguished by looking at the dual action on the
type II graphs. It is also possible to distinguish subfactors by investigating
automorphisms appearing in the irreducible decomposition of the relevant sector (or
bimodule).
