Abstract
We introduce a duality on complex flag manifolds that extendsthe usual point-hyperplane duality of complex projective spaces. Thishas consequences for the structure of the linear cycle spaces of flagdomains, especially when those flag domains are not measurable.
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De Siebenthal, J.: Sur les groupes de Lie compacts non connexes, Comment. Math. Helv. 31 (1956–57), 41–89.
Gray, A. and Wolf, J. A.: Homogeneous spaces defined by Lie group automorphisms I, II, J. Differential Geom. 2(1968), 77–114 and 115–159.
Wolf, J. A.: The action of a real semisimple group on a complex flag manifold, I: Orbit structure and holomorphic arc components, Bull. Amer. Math. Soc. 75(1969), 1121–1237.
Wolf, J. A.: The Stein condition for cycle spaces of open orbits on complex flag manifolds, Ann. of Math. (2) 136(1992), 541–555.
Wolf, J. A.: Exhaustion functions and cohomology vanishing theorems for open orbits on complex flag manifolds, Math. Res. Lett. 2(1995), 179–191.
Wolf, J. A. and Zierau, R.: Holomorphic double fibration transforms, in R. Doran and V. S. Varadarajan (eds), The Mathematical Legacy of Harish-Chandra, Proc. Sympos. Pure Math., Amer. Math. Soc., Providence, R.I., to appear.
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Huckleberry, A.T., Wolf, J.A. Flag Duality. Annals of Global Analysis and Geometry 18, 331–340 (2000). https://doi.org/10.1023/A:1006727207520
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DOI: https://doi.org/10.1023/A:1006727207520