Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Calculs explicites dans une alg\`{e}bre de Lie semi-simple effectu\'{e}s
  avec GAP4   In \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}.

27
The categories of this paper are: comp-gas
35
The categories of this paper are: mtrl-th
13
The categories of this paper are: quant-ph
23
The categories of this paper are: solv-int
0
The categories of this paper are: hep-ph
20
The categories of this paper are: acc-phys
5
The categories of this paper are: gr-qc
32
The categories of this paper are: atom-ph
34
The categories of this paper are: chem-ph
3
The categories of this paper are: physics
31
The categories of this paper are: ao-sci
19
The categories of this paper are: eess
28
The categories of this paper are: alg-geom
1
The categories of this paper are: cs
30
The categories of this paper are: q-alg
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The categories of this paper are: stat