Simplicity of vacuum modules and associated varieties
[Simplicité des algèbres vertex affines et variétés associées]
Journal de l’École polytechnique — Mathématiques, Tome 8 (2021), pp. 169-191.

Dans cet article, nous démontrons que l’algèbre vertex affine universelle associée à une algèbre de Lie simple 𝔤 est simple si et seulement si la variété associée à son unique quotient simple est égale à 𝔤 * . Nous en déduisons un résultat analogue pour la réduction quantique de Drinfeld-Sokolov appliquée à l’algèbre vertex affine universelle.

In this note, we prove that the universal affine vertex algebra associated with a simple Lie algebra 𝔤 is simple if and only if the associated variety of its unique simple quotient is equal to 𝔤 * . We also derive an analogous result for the quantized Drinfeld-Sokolov reduction applied to the universal affine vertex algebra.

Reçu le :
Accepté le :
Publié le :
DOI : 10.5802/jep.144
Classification : 17B69
Keywords: Associated variety, affine Kac-Moody algebra, affine vertex algebra, singular vector, affine $W$-algebra
Mot clés : Variété associée, algèbre de Kac-Moody, algèbre vertex affine, vecteur singulier, $W$-algèbre affine

Tomoyuki Arakawa 1 ; Cuipo Jiang 2 ; Anne Moreau 3

1 Research Institute for Mathematical Sciences, Kyoto University Kyoto, 606-8502, Japan
2 School of Mathematical Sciences, Shanghai Jiao Tong University Shanghai, 200240, China
3 Faculté des Sciences d’Orsay, Université Paris-Saclay 91405 Orsay, France
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits
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Tomoyuki Arakawa; Cuipo Jiang; Anne Moreau. Simplicity of vacuum modules and associated varieties. Journal de l’École polytechnique — Mathématiques, Tome 8 (2021), pp. 169-191. doi : 10.5802/jep.144. https://jep.centre-mersenne.org/articles/10.5802/jep.144/

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