Holomorphic language for \(\overline\partial\)-cohomology and representations of real semisimple Lie groups. (English) Zbl 0808.55006

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, 103-115 (1993).
The author describes a continuous version of Čech cohomology, related to special Stein coverings, indexed by a differentiable manifold, of some complex manifolds, e.g. flag manifolds or pseudo Hermitian symmetric manifolds. Applications are given to hyperfunctions, non-holomorphic discrete series for \(\text{SU}(2,1)\), Speh representations of \(\text{SL} (2n,\mathbb{R})\).
For the entire collection see [Zbl 0780.00026].
Reviewer: G.Roos (Poitiers)


55N30 Sheaf cohomology in algebraic topology
32W05 \(\overline\partial\) and \(\overline\partial\)-Neumann operators
22E46 Semisimple Lie groups and their representations
32M15 Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras (complex-analytic aspects)
32A45 Hyperfunctions