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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

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 $ {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 ``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