Admissible representations and geometry of flag manifolds. (English) Zbl 0822.22010

Wolf, Joseph A.

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)

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