Linear cycle spaces in flag domains

Citation
Ja. Wolf et R. Zierau, Linear cycle spaces in flag domains, MATH ANNAL, 316(3), 2000, pp. 529-545
Citations number
16
Categorie Soggetti
Mathematics
Journal title
MATHEMATISCHE ANNALEN
ISSN journal
00255831 → ACNP
Volume
316
Issue
3
Year of publication
2000
Pages
529 - 545
Database
ISI
SICI code
0025-5831(200003)316:3<529:LCSIFD>2.0.ZU;2-6
Abstract
Let Z = G/Q, a complex flag manifold, where G is a complex semisimple Lie g roup and Q is a parabolic subgroup. Fix a real form G(0) subset of G and co nsider the linear cycle spaces M-D, spaces of maximal compact linear subvar ieties of open orbits D = G(0)(z) subset of Z. In general M-D is a Stein ma nifold. Here the exact structure of M-D is worked out when G(0) is a classi cal group that corresponds to a bounded symmetric domain B. In that case M- D is biholomorphic to B if a certain double fibration is holomorphic, is bi holomorphic to B x (B) over bar otherwise. There are also a number of struc tural results that do nut require G(0) to be classical.