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Funktsional. Anal. i Prilozhen., 2007, Volume 41, Issue 4, Pages 60–69 (Mi faa2879)  

$K$-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

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

DOI: https://doi.org/10.4213/faa2879

Full text: PDF file (246 kB)
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English version:
Functional Analysis and Its Applications, 2007, 41:4, 295–302

Bibliographic databases:

UDC: 512.81+517.58
Received: 31.03.2006

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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\jour Funktsional. Anal. i Prilozhen.
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\pages 60--69
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