999 Heldermann Verlag Z-gradations of Lie Algebras and Innnitesimal Generators
نویسنده
چکیده
In this paper we arrive at explicit formulae for the innnitesi-mal generators of the action of a complex simple Lie group G on the mani-fold M = G=P where P is a maximal parabolic subgroup. These formulae are obtained by assuming that local coordinates on M are furnished by the nilpotent subalgebra n complementary to the maximal parabolic subalgebra p corresponding to P. For the classical isogeny classes A r , B r , C r , and D r , the components of the innnitesimal generators are never worse than quartic polynomials in the coordinate functions, but for the exceptional cases, G 2 , F 4 , and E r , higher-degree polynomials frequently occur.
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