Separable representations for automorphism groups of infinite symmetric spaces

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Abstract

In this paper we consider the separable unitary representations for the automorphism groups of the classical infinite rank (Finsler) symmetric spaces defined by Schatten p-classes (often referred to as restricted groups). Following earlier work of Ol'shanskii and Voiculescu, it is shown that the spherical representations are always type I, the form of the irreducible spherical functions is determined, and their analyticity established. Using an intuitive geometric argument, it is shown that the real spherical functions extend to the Hilbert-Schmidt limit and never beyond. This yields a complete determination of the separable representations for groups corresponding to p-classes with p > 2.

Original languageEnglish (US)
Pages (from-to)1-26
Number of pages26
JournalJournal of Functional Analysis
Volume90
Issue number1
DOIs
StatePublished - 1990

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Spherical Functions
Symmetric Spaces
Automorphism Group
Finsler Space
Unitary Representation
Analyticity
Hilbert
Intuitive
Class
Form

ASJC Scopus subject areas

  • Analysis

Cite this

Separable representations for automorphism groups of infinite symmetric spaces. / Pickrell, Douglas M.

In: Journal of Functional Analysis, Vol. 90, No. 1, 1990, p. 1-26.

Research output: Contribution to journalArticle

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