## 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.

### MSC:

 53C35 Differential geometry of symmetric spaces 32E10 Stein spaces
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### References:

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