Abstract
A real reductive Lie group G 0 acts on complex flag manifolds G/Q, where Q is a parabolic subgroup of the complexification G of G 0. The open orbits D = G 0(x) include the homogeneous complex manifolds of the form G 0/V 0 where V 0= G 0∩Q x the centralizer of a torus; those are the G 0-homogeneous pseudo-kähler manifolds. For an appropriate choice K 0 maximal compact subgroup of G 0, the orbit Y=K 0(x) is a maximal compact complex submanifold of D. The “cycle space” M D =gY ∣ g ∈ G and gY ⊂ D, space of maximal compact linear subvarieties of D, has a natural complex structure. M D plays important roles in the theory of moduli of compact kähler manifolds and in automorphic cohomology theory. Here we sketch a brief exposition of this interesting mathematical topic.
to Bert Kostant on the occasion of his sixty-fifth birthday
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Wolf, J.A. (1994). Compact Subvarieties in Flag Domains. In: Brylinski, JL., Brylinski, R., Guillemin, V., Kac, V. (eds) Lie Theory and Geometry. Progress in Mathematics, vol 123. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0261-5_22
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DOI: https://doi.org/10.1007/978-1-4612-0261-5_22
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