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Journal of Lie Theory 22 (2012), No. 3, 883--886
Copyright Heldermann Verlag 2012

On the Conjugacy of Maximal Unipotent Subgroups of Real Semisimple Lie Groups

Hassan Azad
Dept. of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia

Indranil Biswas
School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay 400005, India

The existence of closed orbits of real algebraic groups on real algebraic varieties is established. As an application, it is shown that if G is a real reductive linear group with Iwasawa decomposition G = KAN, then every unipotent subgroup of G is conjugate to a subgroup of N.

Keywords: Closed orbit, unipotent subgroup, real algebraic group.

MSC: 14L30, 20G20, 22E15, 17B81

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