On the dimension of the sheets of a reductive Lie algebra

Details On the dimension of the sheets of a reductive Lie algebra On the dimension of the sheets of a reductive Lie algebra

2007-11-17

arxiv.org/abs/0711.2735v3

Journal of Lie Theory 18, 3 (2008) 671--696

Mathematics

Representation Theory

29 pages

Scientific paper

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.

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