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On the cohomology of locally symmetric Hermitian spaces. (English) Zbl 0539.22008
Sémin. d’Algèbre P. Dubreil et M.-P. Malliavin, 35ème Année, Proc., Paris 1982, Lect. Notes Math. 1029, 55-98 (1983).
[For the entire collection see Zbl 0519.00007.]
The paper deals with the cohomology of locally symmetric spaces. We generalize the results of Y. Matsushima and S. Murakami [Ann. Math. (2) 78, 365–416 (1963; Zbl 0125.10702)]. The method of proof uses complexes of differential operators corresponding to the classical Bernstein-Gelfand-Gelfand-resolution of Verma-modules.
Reviewer: Gerd Faltings

22E40 Discrete subgroups of Lie groups
32M15 Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras (complex-analytic aspects)