
Journal of Lie Theory 22 (2012), No. 3, 883886 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 hassanaz@kfupm.edu.sa Indranil Biswas School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay 400005, India indranil@math.tifr.res.in 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 [ Fulltextpdf (176 KB)] for subscribers only. 