# Computations with nilpotent orbits in SLA

@article{Graaf2013ComputationsWN, title={Computations with nilpotent orbits in SLA}, author={Willem A. de Graaf}, journal={arXiv: Rings and Algebras}, year={2013} }

We report on some computations with nilpotent orbits in simple Lie algebras of exceptional type within the SLA package of GAP4. Concerning reachable nilpotent orbits our computations firstly confirm the classification of such orbits in Lie algebras of exceptional type by Elashvili and Grelaud, secondly they answer a question by Panyushev, and thirdly they show in what way a recent result of Yakimova for the Lie algebras of classical type extends to the exceptional types. The second topic of…

## 7 Citations

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. Let G be a simple algebraic group deﬁned over C and let e be a rigid nilpotent element in g = Lie( G ). In this paper we prove that the ﬁnite W -algebra U ( g , e ) admits either one or two…

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Let g = Lie(G) be the Lie algebra of a simple algebraic group G over an algebraically closed field of characteristic 0. Let e be a nilpotent element of g and let g_e = Lie(G_e) where G_e stands for…

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. Let g = g ¯0 ⊕ g ¯1 be a basic classical Lie superalgebra over C , e ∈ g ¯0 a nilpotent element and g e the centralizer of e in g . We study various properties of nilpotent elements in g , which…

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Let $G$ be a simple simply connected algebraic group over an algebraically closed field $k$ of characteristic $p>0$ with $\mathfrak{g}=\text{Lie}(G)$ . We discuss various properties of nilpotent…

### MULTIPLICITY-FREE PRIMITIVE IDEALS ASSOCIATED WITH RIGID NILPOTENT ORBITS

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Let G be a simple algebraic group defined over ℂ. Let e be a nilpotent element in $$ \mathfrak{g} $$ = Lie(G) and denote by U ($$ \mathfrak{g} $$, e) the finite W-algebra associated with the pair ($$…

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