|
| | | | |
| | | |
| Stat |
Members: 3645
Articles: 2'500'096
Articles rated: 2609
19 April 2024 |
|
| | | | |
|
Article overview
| |
|
|
Indice du normalisateur du centralisateur d'un element nilpotent dans une algebre de Lie semi-simple | | Anne Moreau
; | | Date: |
15 Jul 2004 | | Subject: | Representation Theory MSC-class: 22E46,22E47,22E60,14A10,14A20 | math.RT | | Abstract: | The index of a complex Lie algebra is the minimal codimension of its coadjoint orbits. Let us suppose $g$ semisimple, then its index, ${
m ind} g$, is equal to its rank, ${
m rk g}$. The goal of this paper is to establish a simple general formula for the index of $
(g^{xi})$, for $xi$ nilpotent, where $
(g^{xi})$ is the normaliser in $g$ of the centraliser $g^{xi}$ of $xi$. More precisely, we have to show the following result, conjectured by D. Panyushev cite{Panyushev} : $${
m ind}
(g^{xi}) = {
m rk g}-dim z(g^{xi}),$$ where $z(g^{xi})$ is the center of $g^{xi}$. D. Panyushev obtained in cite{Panyushev} the inequality hbox{${
m ind}
(g^{xi}) geq {
m rg g}-dim z(g^{xi})$} and we show that the maximality of the rank of a certain matrix with entries in the symmetric algebra ${cal S}(g^{xi})$ implies the other inequality. The main part of this paper consists of the proof of the maximality of the rank of this matrix. | | Source: | arXiv, math.RT/0407277 | | Services: | Forum | Review | PDF | Favorites | |
|
|
No review found.
Did you like this article?
Note: answers to reviews or questions about the article must be posted in the forum section.
Authors are not allowed to review their own article. They can use the forum section.
browser Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)
|
| |
|
|
|
|
News, job offers and information for researchers and scientists:
| |
REGISTER