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Locally compact groups whose conjugation representations satisfy a Kazhdan type property or have countable support

Published online by Cambridge University Press:  24 October 2008

Eberhard Kaniuth  and
Annette Markfort
Eberhard Kaniuth
Affiliation:
Fachbereich Mathematik/Informatik, Universität Paderborn, D-33095 Paderborn, Germany
Annette Markfort
Affiliation:
Fachbereich Mathematik/Informatik, Universität Paderborn, D-33095 Paderborn, Germany
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Extract

For a locally compact group G with left Haar measure and modular function δ the conjugation representation γG of G on L2(G) is defined by

f ∈ L2(G), x, y ∈ G. γG has been investigated recently (see [19, 20, 21, 24, 32, 35]). For semi-simple Lie groups, a related representation has been studied in [25]. γG is of interest not least because of its connection to questions on inner invariant means on L∞(G). In what follows suppγG denotes the support of γG in the dual space Ĝ, that is the closed subset of all equivalence classes of irreducible representations which are weakly contained in γG. The purpose of this paper is to establish relations between properties such as a variant of Kazhdan's property and discreteness or countability of supp γG and the structure of G.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 116 , Issue 1 , July 1994 , pp. 79 - 97
Copyright
Copyright © Cambridge Philosophical Society 1994

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