We will review a notion of Morita equivalence between
subfactors, which is a variation of Morita equivalence in ring
and module theory. The main result is stated as follows: for
arbitrary two Morita equivalent subfactors of hyperfinite II$_1$
factors with finite Jones index and finite depth we can always
choose a finite dimensional non-degenerate commuting square which
gives rise to the subfactors isomorphic to the original ones.
As an application of Morita equivalence between subfactors in
connection with recent developments of theory of finite
dimensional weak $C^*$-Hopf algebras, we will make a brief
comment about the 3-dimensional topological quantum field
theories obtained from subfactors with finite index and finite
depth.
(C)2000 Nobuya Sato [e-mail:nobuya@mi.cias.osakafu-u.ac.jp]