Journal of Lie Theory

no. 2
Remark on the Complexified Iwasawa Decomposition
Journal of Lie Theory, Volume 12 (2002) no. 2, pp. 617-618
\def\C{\mathbb{C}} \def\R{\mathbb{R}} Let $G_\R$ be a real form of a complex semisimple Lie group $G_\C$\,. We identify the complexification $K_\C A_\C N_\C \subset G_\C$ of an Iwasawa decomposition $G_\R = K_\R A_\R N_\R$ as $\{g \in G_\C \mid gB \in \Omega\}$ where $B \subset G_\C$ is a Borel subgroup of $G_\C$ that contains $A_\R N_\R$ and $\Omega$ is the open $K_\C$--orbit on $G_\C /B$. This is done in the context of subsets $K_\C R_\C \subset G_\C\,$, where $R_\C$ is a parabolic subgroup of $G_\C$ defined over $\R$, and the open $K_\C$--orbits on complex flag manifolds $G_\C /Q$.
DOI: 10.5802/jolt.286
Classification: 22E46, 22E10
Keywords: complex semisimple Lie group, Iwasawa decomposition, complex flag manifolds 
@article{JOLT_2002_12_2_a20,
     author = {A. R. Sinton and J. A. Wolf},
     title = {Remark on the {Complexified} {Iwasawa} {Decomposition}},
     journal = {Journal of Lie Theory},
     pages = {617--618},
     year = {2002},
     volume = {12},
     number = {2},
     doi = {10.5802/jolt.286},
     zbl = {0993.22013},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.286/}
}
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A. R. Sinton; J. A. Wolf. Remark on the Complexified Iwasawa Decomposition. Journal of Lie Theory, Volume 12 (2002) no. 2, pp. 617-618. doi: 10.5802/jolt.286

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