Geodesic
A Note on the Linear Cycle Space for Groups of Hermitian Type
Joseph A. Wolf1 ; Roger Zierau2, 3
1Dept. of Mathematics, University of California, Berkeley, CA 94720-3840, U.S.A.
2Dept. of Mathematics, Oklahoma State University, Stillwater, OK 74078-1058, U.S.A.
3[
Journal of Lie Theory, Tome 13 (2003) no. 1, pp. 189-191 
Joseph A. Wolf; Roger Zierau. A Note on the Linear Cycle Space for Groups of Hermitian Type. Journal of Lie Theory, Tome 13 (2003) no. 1, pp. 189-191. http://geodesic.mathdoc.fr/item/JOLT_2003_13_1_a10/
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     author = {Joseph A. Wolf and Roger Zierau},
     title = {A {Note} on the {Linear} {Cycle} {Space} for {Groups} of {Hermitian} {Type}},
     journal = {Journal of Lie Theory},
     pages = {189--191},
     year = {2003},
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     url = {http://geodesic.mathdoc.fr/item/JOLT_2003_13_1_a10/}
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Voir la notice de l'article provenant de la source Heldermann Verlag

Let $G_0$ be a simple Lie group of hermitian type and let $B$ denote the corresponding hermitian symmetric space. The linear cycle space for any nonholomorphic type flag domain of $G_0$ is biholomorphic to $B \times \overline{B}$. When $G_0$ is a classical group this was proved by the authors in a paper published several years ago [Math. Annalen 316 (2000) 529--545]. Here we show that the result follows for arbitrary groups of hermitian type. This is done without case by case arguments by combining results from the paper cited above with recent results of A. T. Huckleberry and the first author [Duke Math. J. 120 (2003) 229--249].