Abstract
Recently, Auslander and Brezin developed a technique of distinguishing between certain unitarily equivalent irreducible subspaces of ${L^2}$ 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 âniceâ theory of distinguished subspaces is equivalent to the existence of square integrable representations for the group.
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