Calculs explicites dans une algèbre de Lie semi-simple effectués avec GAP4

dc.creatorMoreau, Anne
dc.date2005-03-01
dc.date.accessioned2026-07-07T05:17:35Z
dc.date.available2026-07-07T05:17:35Z
dc.descriptionIn \cite{indice}, we show the following result, conjectured by D. Panyushev \cite{Panyushev}, for $\g$ a semisimple Lie algebra: {\rm ind} \n(\g^{e}) = {\rm rk} \g-\dim \z(\g^{e}, where $\n(\g^{e})$ and $\z(\g^{e})$ are, respectively, the normaliser and the centre of the centraliser $\g^{e}$ of a nilpotent element $e$. This result is proved in \cite{indice} when $\g$ is a classical simple Lie algebra and when $e$ satisfies a certain property $(P)$. We present in this paper the computations, made using GAP4, which prove that distinguished, non-regular, nilpotent orbits in $E\_6$, $E\_7$, $E\_8$ and $F\_4$ satisfy the property $(P)$. This work completes the proof, presented in \cite{indice}, of the equality (\ref{princ}). The complete proof of this result was already presented in \cite{indice\_arxiv}.
dc.description34 pages en français
dc.identifierhttps://arxiv.org/abs/math/0503019
dc.identifierhttp://arxiv.org/abs/math/0503019
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/74357
dc.subjectRepresentation Theory
dc.subject22-04 22E60
dc.titleCalculs explicites dans une algèbre de Lie semi-simple effectués avec GAP4
dc.typetext

Files

Collections