Journal of Lie TheoryVol. 12, No. 2, pp. 617--618 (2002)
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Journal of Lie Theory Vol. 12, No. 2, pp. 617--618 (2002) |
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Remark on the Complexified Iwasawa DecompositionAndrew R. Sinton and Joseph A. WolfAndrew R. SintonDepartment of Mathematics University of California Berkeley, CA 94720-3840, USA sinton@math.berkeley.edu, and Joseph A. Wolf Department of Mathematics University of California Berkeley, CA 94720-3840, USA jawolf@math.berkeley.edu Abstract: 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 $G_\C /Q$ Full text of the article:
Electronic fulltext finalized on: 6 May 2002. This page was last modified: 21 May 2002.
© 2002 Heldermann Verlag
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