Noyau de Cauchy-Szegö d'un espace symétrique de type Cayley
Annales de l'Institut Fourier, Tome 48 (1998) no. 1, p. 97-132
Dans cet article, en utilisant les algèbres de Jordan euclidiennes, nous étudions l’espace de Hardy H 2 (Ξ) d’un espace symétrique de type Cayley =G/H. Nous montrons que le noyau de Cauchy-Szegö de H 2 (Ξ) s’exprime comme somme d’une série faisant intervenir la fonction c de Harish-Chandra de l’espace symétrique riemannien D=G/K, la fonction c de l’espace symétrique c-dual 𝒩 de et les fonctions sphériques de l’espace symétrique ordonné 𝒩. Nous établissons, dans le cas où la dimension de l’algèbre de Jordan associée à est un multiple de son rang, un isomorphisme entre l’espace de Hardy H 2 (Ξ) (non-commutatif) et l’espace de Hardy classique H 2 (D×D) (commutatif) du bi-disque. Nous obtenons ainsi une deuxième formule pour le noyau de Cauchy-Szegö.
In this paper, by using the Euclidean Jordan algebras, we study the Hardy space H 2 (Ξ) of a symmetric space of Cayley type =G/H. We show that the Cauchy-Szegö kernel of H 2 (Ξ) expresses as a series using the Harish-Chandra c-function of the Riemannian symmetric space D=G/K, the c-function of the c-dual symmetric space 𝒩 of and spherical functions of the ordered symmetric space 𝒩. We give, in the case of the dimension of the Jordan algebra associated to being a multiple of its rank, the relation between the (non-commutative) Hardy space H 2 (Ξ) and the classical (commutative) Hardy space H 2 (D×D) of the bidisc. And we obtain another formula for the Cauchy-Szegö kernel.
@article{AIF_1998__48_1_97_0,
     author = {Chadli, Mohammed},
     title = {Noyau de Cauchy-Szeg\"o d'un espace sym\'etrique de type Cayley},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {48},
     number = {1},
     year = {1998},
     pages = {97-132},
     doi = {10.5802/aif.1612},
     zbl = {0920.43008},
     mrnumber = {99b:22022},
     language = {fr},
     url = {http://www.numdam.org/item/AIF_1998__48_1_97_0}
}
Chadli, Mohammed. Noyau de Cauchy-Szegö d'un espace symétrique de type Cayley. Annales de l'Institut Fourier, Tome 48 (1998) no. 1, pp. 97-132. doi : 10.5802/aif.1612. https://www.numdam.org/item/AIF_1998__48_1_97_0/

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