Norm estimates for unitarizable highest weight modules
Annales de l'Institut Fourier, Volume 49 (1999) no. 4, p. 1241-1264

We consider families of unitarizable highest weight modules ( λ ) λL on a halfline L. All these modules can be realized as vector valued holomorphic functions on a bounded symmetric domain 𝒟, and the polynomial functions form a dense subset of each module λ , λL. In this paper we compare the norm of a fixed polynomial in two Hilbert spaces corresponding to two different parameters. As an application we obtain that for all λL the module of hyperfunction vectors λ - can be realized as the space of all holomorphic functions on 𝒟.

Nous considérons des familles de modules de poids dominant unitarisables ( λ ) λL sur une demi-droite L. Ces modules peuvent être réalisés comme des fonctions holomorphes à valeurs vectorielles sur un domaine borné symétrique 𝒟. Les fonctions polynomiales constituent un sous-ensemble dense de chaque λ , λL. Dans ce travail nous comparons les normes d’un polynôme fixé dans deux espaces de Hilbert correspondant à deux paramètres différents. Comme application nous montrons que, pour tout λL, le module de vecteurs hyperfonctions λ - peut être réalisé comme l’espace des fonctions holomorphes sur 𝒟.

@article{AIF_1999__49_4_1241_0,
     author = {Kr\"otz, Bernhard},
     title = {Norm estimates for unitarizable highest weight modules},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {49},
     number = {4},
     year = {1999},
     pages = {1241-1264},
     doi = {10.5802/aif.1716},
     zbl = {0930.22013},
     mrnumber = {2001i:22013},
     language = {en},
     url = {http://www.numdam.org/item/AIF_1999__49_4_1241_0}
}
Norm estimates for unitarizable highest weight modules. Annales de l'Institut Fourier, Volume 49 (1999) no. 4, pp. 1241-1264. doi : 10.5802/aif.1716. http://www.numdam.org/item/AIF_1999__49_4_1241_0/

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