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Journal of Lie Theory 13 (2003), No. 1, 189--191
Copyright Heldermann Verlag 2003

A Note on the Linear Cycle Space for Groups of Hermitian Type

Joseph A. Wolf
Dept. of Mathematics, University of California, Berkeley, CA 94720-3840, U.S.A.

Roger Zierau
Dept. of Mathematics, Oklahoma State University, Stillwater, OK 74078-1058, U.S.A.


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].

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