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Sbornik: Mathematics, 2000, Volume 191, Issue 5, Pages 683–715
DOI: https://doi.org/10.1070/sm2000v191n05ABEH000477 (Mi sm477) 		 
This article is cited in 23 scientific papers (total in 23 papers)

Matrix analogues of the beta function and Plancherel's formula for Berezin kernel representations

Yu. A. Neretin

Moscow State Institute of Electronics and Mathematics
English version PDF (414 kB) Citations (23)
References:
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DOI: https://doi.org/10.1070/sm2000v191n05ABEH000477
Abstract: Ten series of matrix integrals (over non-compact Riemannian symmetric spaces) imitating the standard beta function are constructed. This is a broad generalization of Hua Loo Keng's integrals (1958) and Gindikin's B-integrals (1964). As a consequence Plancherel's formula for the Berezin kernel representations of classical groups is obtained in explicit form. Matrix models of non-compact Riemannian symmetric spaces are also discussed.
Received: 15.03.1999
Russian version:
Matematicheskii Sbornik, 2000, Volume 191, Number 5, Pages 67–100
DOI: https://doi.org/10.4213/sm477
Bibliographic databases:
UDC: 519.46
MSC: 33A75, 53C35
Language: English
Original paper language: Russian
Citation: Yu. A. Neretin, “Matrix analogues of the beta function and Plancherel's formula for Berezin kernel representations”, Mat. Sb., 191:5 (2000), 67–100; Sb. Math., 191:5 (2000), 683–715
Citation in format AMSBIB
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    • This publication is cited in the following 23 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Russian version PDF:255
    English version PDF:15
    References:114
    First page:3
     
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