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Journal of Lie Theory 14 (2004), No. 1, 287--316
Copyright Heldermann Verlag 2004
The Structure of Parabolic Subgroups
Kenneth D. Johnson
The University of Georgia,
Athens, GA 30602,
U.S.A.,
ken@math.uga.edu
Suppose G is a real connected simple noncompact Lie group with (using
standard notation) Iwasawa decomposition G = KAN. If M is the intersection
of Z(A) and 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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