Les sous-algebres de Cartan reelles et la frontiere d'une orbite ouverte dans une variete de drapeaux |
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Authors: | Jacques Carmona |
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Institution: | (1) U. E. R. Marseille-Luminy, 70, Route Léon Lachamp, 13288 Marseille Cedex 2, France |
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Abstract: | We show how the non compact imaginary roots of a non compact real semi-simple Lie algebra with respect to a Cartan subalgebra to allows us, alike the real roots of, to give a complete classification of the G-conjugacy classes of Cartan subalgebras of if Gc is a complex connected group whose algebra is the complexified of, if B is a Borel subgroup of Gc and G the analytic subgroup of Gc corresponding to the subalgebra of, we determine the G-orbits of codimension one in the boundary of an open G-orbit of the complex flag manifold Gc/B. If is a maximally compact Cartan subalgebra of contained in, we show how the imaginary non compact simple roots of allows us to determine such orbits. |
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