Nilpotent Orbits and Theta-stable Parabolic Subalgebras
نویسنده
چکیده
In this work, we present a new classification of nilpotent orbits in a real reductive Lie algebra g under the action of its adjoint group. Our classification generalizes the Bala-Carter classification of the nilpotent orbits of complex semisimple Lie algebras. Our theory takes full advantage of the work of Kostant and Rallis on pC , the “complex symmetric space associated with g”. The Kostant-Sekiguchi correspondence, a bijection between nilpotent orbits in g and nilpotent orbits in pC , is also used. We identify a fundamental set of noticed nilpotents in pC and show that they allow us to recover all other nilpotents. Finally, we study the behaviour of a principal orbit, that is an orbit of maximal dimension, under our classification. This is not done in the other classification schemes currently available in the literature.
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