Let σ be an isometric representation of N^d on a Hilbert space H. We induce σ to an isometric representation V of R₊^d on another Hilbert space K. We show that the map σ --> V, restricted to strongly pure isometric representations, preserves index and irreducibility. As an application, we show that, for every k in {0, 1,2,...} ∪ {∞}, there is a continuum of prime multiparameter CCR flows with index k.

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