Some amazing properties of spherical nilpotent orbits
| dc.creator | Panyushev, Dmitri I. | |
| dc.date | 2002-06-25 | |
| dc.date | 2002-07-15 | |
| dc.date.accessioned | 2026-07-07T04:49:21Z | |
| dc.date.available | 2026-07-07T04:49:21Z | |
| dc.description | 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 $G_2$ 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. | |
| dc.description | 22 pages, Latex. A minor point in the proof of 3.5 is corrected | |
| dc.identifier | https://arxiv.org/abs/math/0206265 | |
| dc.identifier | http://arxiv.org/abs/math/0206265 | |
| dc.identifier | Math. Zeitschrift, 245 (2003), 557-580 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/64393 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Representation Theory | |
| dc.title | Some amazing properties of spherical nilpotent orbits | |
| dc.type | text |