Invariant spaces of holomorphic functions on symmetric Siegel domains

In this paper we consider a symmetric Siegel domain D and some natural representations of the Möbius group G of its biholomorphisms and of the group Aff of its affine biholomorphisms. We provide a classification of the affinely-invariant semi-Hilbert spaces (satisfying some natural additional assumptions) on tube domains, and slightly improve the classification of Möbius-invariant semi-Hilbert spaces on general domains.