2002/06/30 by Dmitri I. Panyushev
Mathematics · #math.AG #math.RT
published as Math. Zeitschrift, 245 (2003), 557-580 · 22 pages, Latex. A minor point in the proof of 3.5 is corrected
arxiv created 2002/07/15 · arxiv updated 2009/11/30
Let \g be simple Lie algebra. We give a conceptual proof for the fact that the nilpotent orbits of height 3 are spherical. It is shown that if the highest root of \g is fundamental, then \g has a specific nilpotent orbit of height 3. This orbit satisfies several interesting relations. Moreover, it can be used for an intrinsic construction of a G2 grading in \g. We also discuss an approach to describing the algebra of covariants on a nilpotent orbit. For the nilpotent orbits of height 2, it is shown that the algebra of regular functions is a free module over the algebra of covariants. For the nilpotent orbits of height 3, a conjectural description of the algebra of covariants is given. This description is compatible with all previously known examples.