Given a wavelet in L²(R) for dilation by the positive integer N ≥ 2, there is an associated representation of the Baumslag-Solitar group BS_N, which is the group on two generators a and b satisfying the relation aba^-1=b^N. It is possible to generalize this construction for certain wavelets on more abstract Hilbert spaces, obtaining under appropriate conditions unitary representations W of BS_N. Under these conditions, D. Dutkay showed that there is a probability measure τ on the solenoid Σ_N constructed from the endomorphism z→ z^N on the circle, such that W is equivalent to a unitary representation of BS_N on L²(Σ_N, τ). We discuss a different way of constructing the measure τ, and remark how this method can be used to embed generalizations of the wavelet sets of X. Dai and D. Larson into the solenoid Σ_N. These embeddings in turn can be used to obtain a direct integral decomposition of W. The talk is based on joint work with L. Baggett, N. Larsen, K. Merrill, I. Raeburn, and A. Ramsay.

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