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Recently, Ausländer and Brezin developed a technique of distinguishing between certain unitarily equivalent irreducible subspaces of L2 of the Heisenberg nilmanifold. In this paper we extend the Auslander-Brezin technique to arbitrary induced representations of arbitrary locally compact groups. We then return to nilmanifolds, showing that the existence of a "nice" theory of distinguished subspaces is equivalent to the existence of square integrable representations for the group.doi:10.2307/1997985 fatcat:s6ryp4eksvauvjsjoepbky4iau