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Calculs explicites dans une algèbre de Lie semi-simple effectués avec GAP4 | Anne Moreau
; | Date: |
1 Mar 2005 | Subject: | Representation Theory MSC-class: 22-04 22E60 | math.RT | Affiliation: | IMJ | Abstract: | In cite{indice}, we show the following result, conjectured by D. Panyushev cite{Panyushev}, for $g$ a semisimple Lie algebra: {
m ind}
(g^{e}) = {
m rk} g-dim z(g^{e}, where $
(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 (
ef{princ}). The complete proof of this result was already presented in cite{indice\_arxiv}. | Source: | arXiv, math.RT/0503019 | Services: | Forum | Review | PDF | Favorites |
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