  Several years ago, O. Bratelli and P. Jorgensen developed the concept of
m-systems of filters for dilation by a positive integer N>1 on L^2(R). They
constructed a loop group action on m-systems. By work of Mallat and Meyer,
these m-systems are important in constructing multi-resolution analyses and
wavelets associated to dilation by N and translation by Z on L^2(R). In this
paper, we discuss an extension of this loop-group construction to generalized
filter systems, which we will call ``M-systems,'' associated with generalized
multiresolution analyses. In particular, we show that every multiplicity
function has an associated generalized loop group which acts freely and
transitively on the set of M-systems corresponding to the multiplicity
function. The results of Bratteli and Jorgensen correspond to the case where
the multiplicity function is identically equal to 1.
