We record a lifting theorem for the intertwiner of two S_Ω-isometries which are those subnormal operator tuples whose minimal normal extensions have their Taylor spectra contained in the Shilov boundary of a certain function algebra associated with Ω, Ω being a bounded convex domain in Cⁿ containing the origin. The theorem captures several known lifting results in the literature and yields interesting new examples of liftings as a consequence of its being applicabile to Cartesian products Ω of classical Cartan domains in Cⁿ. Further, we derive intrinsic characterizations of S_Ω-isometries where Ω is a classical Cartan domain of any of the types I, II, III and IV, and we also provide a neat description of an S_Ω-isometry in case Ω is a finite Cartesian product of such Cartan domains.

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