A direct integral decomposition of the wavelet representation

In this paper we use the concept of wavelet sets, as introduced by X. Dai a nd D. Larson, to decompose the wavelet representation of the discrete group associated to an arbitrary nxn integer dilation matrix as a direct integra l of irreducible monomial representations. In so doing we generalize a resu lt of F. Martin and A. Valette in which they show that the wavelet represen tation is weakly equivalent to the regular representation for the Baumslag- Solitar groups.