Journal of Lie Theory, 7(2), 245-267 (1997)

Hardy spaces on two-sheeted covering semigroups

K. Koufany and B. Ørsted

Institut E. Cartan
Université H. Poincaré
B.P. 239
F-54506 Vand{\oe}uvre-Lès-Nancy
France
koufany@iecn.u-nancy.fr

Matematisk Institut
Odense universitet
Campusvej 55
DK-5230 Odense M
Danmark
orsted@imada.ou.dk

Abstract: In this paper we study the minimal complex Lie semigroups associated with three classical series of groups by using a holomorphic continuation of a certain Cayley transform for the group. In particular we show, that for the symplectic group the odd part of the Hardy space on the double cover is isomorphic to the classical Hardy space on the Siegel upper half space corresponding to the symplectic group of twice the rank of the given group.

Keywords: Cauchy-Szegö kernel, Cayley transform, Hardy space, Holomorphic discrete series, Jordan algebra, Ol'shanski\u{\i} semigroup

Classification (MSC91): 22E46, 22E30, 43A17, 43A85

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