Gindikin, Simon 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) Cited in 2 ReviewsCited in 10 Documents MSC: 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 Keywords:continuous Čech cohomology; Stein coverings; flag manifolds; pseudo Hermitian symmetric manifolds; hyperfunctions; discrete series for \(\text{SU}(2,1)\); representations of \(\text{SL} (2n,\mathbb{R})\) PDFBibTeX XMLCite \textit{S. Gindikin}, Contemp. Math. 154, 103--115 (1993; Zbl 0808.55006)