Indice du normalisateur du centralisateur d'un element nilpotent dans une algebre de Lie semi-simple

Simple item page
dc.creatorMoreau, Anne
dc.date2004-07-15
dc.date.accessioned2026-07-07T06:31:41Z
dc.date.available2026-07-07T06:31:41Z
dc.descriptionThe index of a complex Lie algebra is the minimal codimension of its coadjoint orbits. Let us suppose $\g$ semisimple, then its index, ${\rm ind} \g$, is equal to its rank, ${\rm rk \g}$. The goal of this paper is to establish a simple general formula for the index of $\n(\g^ξ)$, for $ξ$ nilpotent, where $\n(\g^ξ)$ is the normaliser in $\g$ of the centraliser $\g^ξ$ of $ξ$. More precisely, we have to show the following result, conjectured by D. Panyushev \cite{Panyushev} : $${\rm ind} \n(\g^ξ) = {\rm rk \g}-\dim \z(\g^ξ),$$ where $\z(\g^ξ)$ is the center of $\g^ξ$. D. Panyushev obtained in \cite{Panyushev} the inequality \hbox{${\rm ind} \n(\g^ξ) \geq {\rm rg \g}-\dim \z(\g^ξ)$} and we show that the maximality of the rank of a certain matrix with entries in the symmetric algebra ${\cal S}(\g^ξ)$ implies the other inequality. The main part of this paper consists of the proof of the maximality of the rank of this matrix.
dc.description54 pages en francais
dc.identifierhttps://arxiv.org/abs/math/0407277
dc.identifierhttp://arxiv.org/abs/math/0407277
dc.identifierBulletin de la SMF 134 (1) (2006) 83-117
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/98680
dc.subjectRepresentation Theory
dc.subject22E46,22E47,22E60,14A10,14A20
dc.titleIndice du normalisateur du centralisateur d'un element nilpotent dans une algebre de Lie semi-simple
dc.typetext

Files

Collections

arXiv