Geodesic
$K$-Finite Matrix Elements of Irreducible Harish-Chandra Modules are Hypergeometric
Funkcionalʹnyj analiz i ego priloženiâ, Tome 41 (2007) no. 4, pp. 60-69

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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, special functions, Heckman–Opdam hypergeometric functions.
Mots-clés : matrix elements 
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     author = {Yu. A. Neretin},
     title = {$K${-Finite} {Matrix} {Elements} of {Irreducible} {Harish-Chandra} {Modules} are {Hypergeometric}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {60--69},
     publisher = {mathdoc},
     volume = {41},
     number = {4},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2007_41_4_a4/}
}
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Yu. A. Neretin. $K$-Finite Matrix Elements of Irreducible Harish-Chandra Modules are Hypergeometric. Funkcionalʹnyj analiz i ego priloženiâ, Tome 41 (2007) no. 4, pp. 60-69. http://geodesic.mathdoc.fr/item/FAA_2007_41_4_a4/