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A Convexity Theorem for Boundariesof Ordered Symmetric Spaces

Published online by Cambridge University Press:  20 November 2018

Joachim Hilgert*
Affiliation:
Mathematisches Institut, TU Clausthal Erzstr. I 38678 Clausthal-Zellerfeld, Germany
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Abstract

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We consider a class of real flag manifolds which occur as Fürstenberg boundaries of ordered symmetric spaces and study the image of associated momentum maps. The presence of the order structure is responsible for much stronger convexity properties than in the general case.

Keywords

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1994

References

[AL92] Arnal, D., and Ludwig, J., La convexité de Vapplication moment d'un groupe de Lie, J. Funct. Anal. 105(1992), 256300.Google Scholar
[At82] Atiyah, M. F., Convexity and commuting Hamiltonians, Bull. London Math. Soc. 14(1982), 115.Google Scholar
[vdB86] van den Ban, E., A convexity theorem for semisimple symmetric spaces, Pacific J. Math. 124(1986), 21-55.Google Scholar
[BE89] Baston, R. J. and Eastwood, M. G., The Penrose Transform, Oxford, 1989.Google Scholar
[BFR90] Bloch, A., Flaschka, H. and Ratiu, T., A convexity theorem for isospectral manifolds ofJacobi matrices in a compact Lie algebra, Duke Math. J. 61(1990), 41-65.Google Scholar
[BR91] Bloch, A. and Ratiu, T., Convexity and integrability. In: Progress in Math. 99, (eds. Donato et al.), Birkhäuser, Basel, 1991.Google Scholar
[CDM88] Condevaux, M., Dazord, P. and Molino, P., Géométrie du moment, Publ. Dép. Math. Univ. Cl.-Bernard-Lyon,(1988).Google Scholar
[Du83] Duistermaat, J. J., Convexity and tightness for restrictions of Hamiltonian functions to fixed point sets of an antisymplectic involution, Trans. Amer. Math. Soc. 275(1983), 417429.Google Scholar
[FH092] Faraut, J., Hilgert, J. and Olafsson, G., Spherical functions on ordered symmetric spaces, Ann. Inst. Fourier, to appear.Google Scholar
[GeSe87] Gelfand, I. M. and V. V. Serganova, , Combinatorial geometries and torus strata on homogeneous compact manifolds, Russian Math. Surveys 42(1987), 133-168.Google Scholar
[GuSt82] Guillemin, V. and Sternberg, S., Convexity properties of the momentum map I, Invent. Math. 67( 1982), 491-513.Google Scholar
[Hi92] Hilgert, J., Convexity properties of Grassmannians, Seminar S. Lie 2(1992), 13-20.Google Scholar
[HiNe93] Hilgert, J. and Neeb, K.-H., Lie semigroups and their applications, LNM 1552, 1993.Google Scholar
[Ki84] Kirwan, F., Convexity properties of the momentum map III, Invent. Math. 77(1984), 547-552.Google Scholar
[Ko73] Kostant, B., On convexity, the Weyl group and the Iwasawa decomposition, Ann. Sci. Ecole Norm. Sup. 6(1973), 413-455.Google Scholar
[LR91] Lu, J. and Ratiu, T., On the nonlinear convexity theorem of Kostant, J. Amer. Math. Soc. 4(1991), 349-363.Google Scholar
[Ne91] Neeb, K.-H., A convexity theorem for semisimple symmetric spaces, Pacific J. Math., to appear.Google Scholar