On the discrete quotients of complex semi-groups. (Sur les quotients discrets de semi-groupes complexes.) (French) Zbl 1241.53048

Summary: Let \(X=G/K\) be an irreducible Hermitian symmetric space of the non-compact type and let \(S\in G^{ \mathbb C }\) be the associated compression semigroup. Let \(\Gamma \subset G\) be a discrete subgroup. We give a sufficient condition for \(\Gamma \setminus S\) to be Stein. Moreover, we show that \(\Gamma \setminus S\) is not Stein in general which disproves a conjecture by Achab, Betten and Krötz.


53C35 Differential geometry of symmetric spaces
32E10 Stein spaces
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