The centralisers of nilpotent elements in classical Lie algebras
| dc.creator | Yakimova, O. S. | |
| dc.date | 2004-07-05 | |
| dc.date | 2004-09-22 | |
| dc.date.accessioned | 2026-07-07T05:09:57Z | |
| dc.date.available | 2026-07-07T05:09:57Z | |
| dc.description | The index of a finite-dimensional Lie algebra $g$ is the minimum of dimensions of stabilisers $g_α$ of elements $α\in g^*$. Let $g$ be a reductive Lie algebra and $z(x)$ a centraliser of a nilpotent element $x\in g$. Elashvili has conjectured that the index of the centraliser $z(x)$ equals the index of $g$, i.e., the rank of $g$. Here Elashvili's conjecture is proved for reductive Lie algebras of classical type. It is shown that in cases $g=gl_n$ and $g=sp_{2n}$ the coadjoint action of $z(x)$ has a generic stabiliser. Also, we give an example of a nilpotent element $x\in so_8$ such that the coadjoint action of $z(x)$ has no generic stabiliser. | |
| dc.description | Replaced with english translation | |
| dc.identifier | https://arxiv.org/abs/math/0407065 | |
| dc.identifier | http://arxiv.org/abs/math/0407065 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/71776 | |
| dc.subject | Representation Theory | |
| dc.title | The centralisers of nilpotent elements in classical Lie algebras | |
| dc.type | text |