Journal of Lie Theory

no. 1
A Note on the Linear Cycle Space for Groups of Hermitian Type
Journal of Lie Theory, Volume 13 (2003) no. 1, pp. 189-191
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].
DOI: 10.5802/jolt.297
Classification: 22E46
Keywords: simple Lie group of hermitian type, linear cycle space, flag domain 
@article{JOLT_2003_13_1_a10,
     author = {J. A. Wolf and R. Zierau},
     title = {A {Note} on the {Linear} {Cycle} {Space} for {Groups} of {Hermitian} {Type}},
     journal = {Journal of Lie Theory},
     pages = {189--191},
     year = {2003},
     volume = {13},
     number = {1},
     doi = {10.5802/jolt.297},
     zbl = {1017.22009},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.297/}
}
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J. A. Wolf; R. Zierau. A Note on the Linear Cycle Space for Groups of Hermitian Type. Journal of Lie Theory, Volume 13 (2003) no. 1, pp. 189-191. doi: 10.5802/jolt.297

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