Linear cycle spaces in flag domains
| Autor: | Roger Zierau, Joseph A. Wolf |
|---|---|
| Rok vydání: | 2000 |
| Předmět: |
Classical group
Mathematics::Complex Variables General Mathematics Flag (linear algebra) High Energy Physics::Phenomenology Mathematical analysis Holomorphic function Fibration Lie group Real form Combinatorics Stein manifold Generalized flag variety Mathematics::Differential Geometry Mathematics::Representation Theory Mathematics |
| Zdroj: | Mathematische Annalen. 316:529-545 |
| ISSN: | 1432-1807 0025-5831 |
| DOI: | 10.1007/s002080050342 |
| Popis: | Let Z = G/Q, a complex flag manifold, where G is a complex semisimple Lie group and Q is a parabolic subgroup. Fix a real form \(G_0 \subset G\) and consider the linear cycle spaces \(M_D\), spaces of maximal compact linear subvarieties of open orbits \(D = G_0(z) \subset Z\). In general \(M_D\) is a Stein manifold. Here the exact structure of \(M_D\) is worked out when \(G_0\) is a classical 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 biholomorphic to \(B \times \overline{B}\) otherwise. There are also a number of structural results that do not require \(G_0\) to be classical. |
| Databáze: | OpenAIRE |
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