Wolf, Joseph A. Admissible representations and geometry of flag manifolds. (English) Zbl 0822.22010 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, 21-45 (1993). The author discusses geometric realizations of various classes of admissible representations of reductive Lie groups. They occur on partially holomorphic cohomology spaces corresponding to partially holomorphic homogeneous vector bundles over real group orbits in complex flag manifolds.For the entire collection see [Zbl 0780.00026]. Reviewer: D.Miličić (Salt Lake City) Cited in 3 Documents MSC: 22E47 Representations of Lie and real algebraic groups: algebraic methods (Verma modules, etc.) 22E46 Semisimple Lie groups and their representations 17B10 Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) 14F05 Sheaves, derived categories of sheaves, etc. (MSC2010) 14F17 Vanishing theorems in algebraic geometry 32A37 Other spaces of holomorphic functions of several complex variables (e.g., bounded mean oscillation (BMOA), vanishing mean oscillation (VMOA)) 32C36 Local cohomology of analytic spaces 32Q45 Hyperbolic and Kobayashi hyperbolic manifolds Keywords:geometric realizations; admissible representations; reductive Lie groups; holomorphic homogeneous vector bundles; real group orbits; complex flag manifolds PDF BibTeX XML Cite \textit{J. A. Wolf}, Contemp. Math. 154, 21--45 (1993; Zbl 0822.22010) OpenURL