Rational subspaces of induced representations and nilmanifolds

Author:
R. Penney

Journal:
Trans. Amer. Math. Soc. **246** (1978), 439-450

MSC:
Primary 22D10; Secondary 22E27

MathSciNet review:
515550

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Abstract: Recently, Auslander and Brezin developed a technique of distinguishing between certain unitarily equivalent irreducible subspaces of 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.

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DOI:
https://doi.org/10.1090/S0002-9947-1978-0515550-X

Article copyright:
© Copyright 1978
American Mathematical Society