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Funktsional'nyi Analiz i ego Prilozheniya, 2007, Volume 41, Issue 4, Pages 60–69
DOI: https://doi.org/10.4213/faa2879 (Mi faa2879) 		 
This article is cited in 1 scientific paper (total in 1 paper)

$K$-Finite Matrix Elements of Irreducible Harish-Chandra Modules are Hypergeometric

Yu. A. Neretinab

a Institute for Theoretical and Experimental Physics (Russian Federation State Scientific Center)
b University of Vienna
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DOI: https://doi.org/10.4213/faa2879
Abstract: We show that each $K$-finite matrix element of an irreducible infinite-dimensional representation of a semisimple Lie group can be obtained from spherical functions by a finite collection of operations. In particular, each matrix element admits a finite expression in the terms of the Heckman–Opdam hypergeometric functions.
Keywords: semisimple Lie groups, Harish-Chandra modules, infinite-dimensional representations, spherical functions, matrix elements, special functions, Heckman–Opdam hypergeometric functions.
Received: 31.03.2006
English version:
Functional Analysis and Its Applications, 2007, Volume 41, Issue 4, Pages 295–302
DOI: https://doi.org/10.1007/s10688-007-0027-6
Bibliographic databases:
Document Type: Article
UDC: 512.81+517.58
Language: Russian
Citation: Yu. A. Neretin, “$K$-Finite Matrix Elements of Irreducible Harish-Chandra Modules are Hypergeometric”, Funktsional. Anal. i Prilozhen., 41:4 (2007), 60–69; Funct. Anal. Appl., 41:4 (2007), 295–302
Citation in format AMSBIB
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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