Let Ω be a bounded symmetric domain of type IV and dimension bigger than four. We show that a Stein manifold of the same dimension as Ω and with the same automorphism group is biholomorphic to Ω.
Laura Geatti, Andrea Iannuzzi, Jean-Jacques Loeb. A characterization of bounded symmetric domains of type IV. Manuscripta Mathematica, 2011, 135 (1-2), pp.183 - 202. ⟨10.1007/s00229-011-0436-y⟩. ⟨hal-03040201⟩