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

Yu. A. Neretin

Sbornik. Mathematics, Tome 191 (2000) no. 5, pp. 683-715

Résumé

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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