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Inductive algebras for trees

Stegel, Giovanni (2004) Inductive algebras for trees. Pacific Journal of Mathematics, Vol. 216 (1), p. 177-200. ISSN 0030-8730. Article.

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Abstract

Let G be a locally compact group and π : G U(H) a unitary representation of G. A commutative subalgebra of BH is called π-inductive when it is stable through conjugation by every operator in the range of π. This concept generalizes Mackey’s definition of a system of imprimitivity for π; it is expected that studying inductive algebras will lead to progress in the classification of realizations of representations on function spaces. In this paper we take as G the automorphism group of a locally finite homogeneous tree; we consider the principal spherical representations of G, which act on a Hilbert space of functions on the boundary of the tree, and classify the maximal inductive algebras of such representations. We prove that, in most cases, there exist exactly two such algebras.

Item Type:Article
ID Code:4748
Status:Published
Refereed:Yes
Uncontrolled Keywords:Inductive algebras, homogeneous trees, nontrivial operators
Subjects:Area 01 - Scienze matematiche e informatiche > MAT/05 Analisi matematica
Divisions:001 Università di Sassari > 03 Istituti > Matematica e fisica
Publisher:University of California, Berkeley
ISSN:0030-8730
Deposited On:02 Nov 2010 15:55

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