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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.,

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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