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Funktsional'nyi Analiz i ego Prilozheniya, 2011, Volume 45, Issue 3, Pages 79–96
DOI: https://doi.org/10.4213/faa3042 (Mi faa3042) 		 
This article is cited in 17 scientific papers (total in 17 papers)

Sphericity and multiplication of double cosets for infinite-dimensional classical groups

Yu. A. Neretinabc

a University of Vienna
b Institute for Theoretical and Experimental Physics
c Moscow State University
Full-text PDF (295 kB) Citations (17)
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DOI: https://doi.org/10.4213/faa3042
Abstract: We construct spherical subgroups in infinite-dimensional classical groups $G$ (usually they are not symmetric and their finite-dimensional analogs are not spherical). We present a structure of a semigroup on double cosets $L\setminus G/L$ for various subgroups $L$ in $G$; these semigroups act in spaces of $L$-fixed vectors in unitary representations of $G$. We also obtain semigroup envelops of groups $G$ generalizing constructions of operator colligations.
Keywords: spherical subgroup, spherical function, unitary representation, operator colligation, characteristic function (transfer function), category representation, inner function.
Received: 24.01.2011
English version:
Functional Analysis and Its Applications, 2011, Volume 45, Issue 3, Pages 225–239
DOI: https://doi.org/10.1007/s10688-011-0025-6
Bibliographic databases:
Document Type: Article
UDC: 517.986.4+512.58+517.984.4+512.546.4
Language: Russian
Citation: Yu. A. Neretin, “Sphericity and multiplication of double cosets for infinite-dimensional classical groups”, Funktsional. Anal. i Prilozhen., 45:3 (2011), 79–96; Funct. Anal. Appl., 45:3 (2011), 225–239
Citation in format AMSBIB
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    • This publication is cited in the following 17 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Функциональный анализ и его приложения Functional Analysis and Its Applications
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