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Dolbeault cohomologies and Zuckerman modules. (English) Zbl 0810.22007
Eastwood, Michael (ed.) et al., The Penrose transform and analytic cohomology in representation theory. AMS-IMS-SIAM summer research conference, June 27 - July 3, 1992, South Hadley, MA, USA. Providence, RI: American Mathematical Society. Contemp. Math. 154, 217-223 (1993).
This paper refers for proofs to the Ph.D. thesis of the author (Harvard, 1992) and discusses relations between Dolbeault cohomology spaces of Fréchet vector bundles over certain open orbits of generalized flag manifolds, and Zuckerman modules. The identification between Dolbeault cohomology and Zuckerman modules, via a “Taylor series map”, is proved for Zuckerman modules associated with finite rank representations.
For the entire collection see [Zbl 0780.00026].
Reviewer: G.Roos (Poitiers)

22E46 Semisimple Lie groups and their representations
32L20 Vanishing theorems
22E30 Analysis on real and complex Lie groups
32W05 \(\overline\partial\) and \(\overline\partial\)-Neumann operators
32L10 Sheaves and cohomology of sections of holomorphic vector bundles, general results
57T10 Homology and cohomology of Lie groups
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