On the dimension of the sheets of a reductive Lie algebra

Anne Moreau (1)

1 D-MATH - Department of Mathematics [ETH Zurich]

Let g be a complex finite dimensional Lie algebra and G its adjoint group. Following a suggestion of A. A. Kirillov, we investigate the dimension of the subsets of linear forms f of g whose coadjoint orbit has dimension 2m. In this paper we focus on the reductive case. If this case the problem reduces to the computation of the dimension of the sheets of g. These sheets are known to be parameterized by the pairs (l,O), up to G-conjugation class, consisting of a Levi subalgebra l of g and a rigid nilpotent orbit O in l. By using this parametrization, we provide dimensions of the above subsets for any m.

Mots clés: rigid nilpotent orbit; reductive Lie algebra; coadjoint orbit; sheet; index; Jordan class; induced nilpotent orbit; rigid nilpotent orbit.

Domaines: Théorie des représentations [math.RT]

Anne Moreau. On the dimension of the sheets of a reductive Lie algebra. Journal of Lie Theory, 2008, 18 (3), pp.671--696. ⟨hal-00188455v3⟩