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manuscripta mathematica

, Volume 112, Issue 4, pp 433–440 | Cite as

Cycles in G-orbits in G -flag manifolds

  • A. HuckleberryEmail author
  • B. Ntatin
Article

Abstract.

There is a natural duality between orbits γ of a real form G of a complex semisimple group G on a homogeneous rational manifold Z=G /P and those κ of the complexification K of any of its maximal compact subgroups K: (γ,κ) is a dual pair if γ∩κ is a K-orbit. The cycle space C(γ) is defined to be the connected component containing the identity of the interior of {g:g(κ)∩γ is non-empty and compact}. Using methods which were recently developed for the case of open G-orbits, geometric properties of cycles are proved, and it is shown that C(γ) is contained in a domain defined by incidence geometry. In the non-Hermitian case this is a key ingredient for proving that C(γ) is a certain explicitly computable universal domain.

Keywords

Geometric Property Dual Pair Compact Subgroup Real Form Natural Duality 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  1. 1.Fakultät für MathematikRuhr–Universität BochumBochumGermany

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