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].


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