The Hua system on irreducible Hermitian symmetric spaces of nontube type
Annales de l'Institut Fourier, Volume 54 (2004) no. 1, pp. 81-127.

Let G/K be an irreducible Hermitian symmetric space of noncompact type. We study a G- invariant system of differential operators on G/K called the Hua system. It was proved by K. Johnson and A. Korányi that if G/K is a Hermitian symmetric space of tube type, then the space of Poisson-Szegö integrals is precisely the space of zeros of the Hua system. N. Berline and M. Vergne raised the question about the nature of the common solutions of the Hua system for Hermitian symmetric spaces of nontube type. In this paper we show that these are exactly the pluriharmonic functions.

Soit G/K un espace hermitien symétrique non compact irréductible. On étudie un système invariant H d’opérateurs differentiels sur G/K. Selon un théorème de K. Johnson et A. Korányi, une fonction sur un espace hermitien symétrique de type tube est annulée par le système 𝐇 de Hua si et seulement si elle est l’intégrale de Poisson-Szegö d’une hyperfonction. N. Berline et M. Vergne ont posé la question de caractériser les fonctions 𝐇 - harmoniques sur les espaces hermitiens de type II. Ici on montre que ce sont les fonctions pluriharmoniques.

DOI: 10.5802/aif.2011
Classification: 32A50,  32W50,  32M15
Keywords: pluriharmonic functions, Hua system, Hermitian symmetric spaces, Siegel domains
Buraczewski, Dariusz 1

1 Uniwersytet Wroclawski, Instytut Matematyczny, Plac Grunwaldzki 2/4, 50-384 Wroclaw, (Pologne)
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Buraczewski, Dariusz. The Hua system on irreducible Hermitian symmetric spaces of nontube type. Annales de l'Institut Fourier, Volume 54 (2004) no. 1, pp. 81-127. doi : 10.5802/aif.2011. https://aif.centre-mersenne.org/articles/10.5802/aif.2011/

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