Journal of Lie Theory
Vol. 14, No. 1, pp. 287--316 (2004)
The Structure of Parabolic Subgroups
Kenneth D. JohnsonKenneth D. Johnson
The University of Georgia
Athens, GA 30602
Abstract: Suppose $G$ is a real connected simple noncompact Lie group with (using standard notation) Iwasawa decomposition $G=KAN$. If $M=Z(A)\cap K$, the group $B=MAN$ is a minimal parabolic subgroup of $G$. Since $A$ is a vector group and $N$ is a simply connected nilpotent group, the topological structure of $B$ is determined by the structure of $M$. When $G$ is a linear group the structure of $M$ is well known. However, if $G$ is not a linear group there is very little available information about $M$. Our purpose here is to give a description of the group $M$ for any connected, simply connected, nonlinear simple group $G$.
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Electronic version published on: 29 Jan 2004. This page was last modified: 1 Sep 2004.