Geodesic
Matrix analogues of the~beta function and Plancherel's formula for Berezin kernel representations
Sbornik. Mathematics, Tome 191 (2000) no. 5, pp. 683-715

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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. 
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     author = {Yu. A. Neretin},
     title = {Matrix analogues of the~beta function and {Plancherel's} formula for {Berezin} kernel representations},
     journal = {Sbornik. Mathematics},
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     url = {http://geodesic.mathdoc.fr/item/SM_2000_191_5_a3/}
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Yu. A. Neretin. Matrix analogues of the~beta function and Plancherel's formula for Berezin kernel representations. Sbornik. Mathematics, Tome 191 (2000) no. 5, pp. 683-715. http://geodesic.mathdoc.fr/item/SM_2000_191_5_a3/