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In this paper we consider a symmetric Siegel domain $D$ and some naturalrepresentations of the M\"obius group $G$ of its biholomorphisms and of thegroup $\mathrm{Aff}$ of its affine biholomorphisms. We provide a completeclassification of the affinely-invariant semi-Hilbert spaces (satisfying somenatural additional assumptions) on tube domains, and improve the classificationof M\"obius-invariant Semi-Hilbert spaces on general domains.

Invariant Spaces of Holomorphic Functions on Symmetric Siegel domains