The Bala-Carter Classification of Nilpotent Orbits of Semisimple Lie Algebras - Rakotoarisoa, Andriamananjara Tantely (Université d'Ottawa / University of Ottawa, 2017)
Conjugacy classes of nilpotent elements in complex semisimple Lie algebras are classified using the Bala-Carter theory. In this theory, nilpotent orbits in g are parametrized by the conjugacy classes of pairs (l,pl) of Levi subalgebras of g and distinguished parabolic subalgebras of [l,l]. In this thesis we present this theory and use it to give a list of representatives for nilpotent orbits in so(8) and from there we give a partition-type parametrization of them.
Keywords: Lie; Algebras; Representation; Theory; Nilpotent; Orbits; Bala-Carter; Dynkin