The intersection between a nilpotent orbit and the Lie algebra of a Borel subgroup is an equidimensional, quasi-affine algebraic variety. Its irreducible components are called orbital varieties. In this Note, we provide criteria to guarantee that an orbital variety is smooth or has a dense orbit for the adjoint action of B. In addition, we point out a possible relation between these two properties.
Lʼintersection entre une orbite nilpotente et lʼalgèbre de Lie dʼun sous-groupe de Borel est une variété algébrique quasi-affine équidimensionnelle. Ses composantes irréductibles sont appelées variétés orbitales. Dans cette Note, on propose des critères pour quʼune variété orbitale soit lisse ou bien possède une orbite dense pour lʼaction adjointe de B. De plus, on souligne un lien possible entre ces deux propriétés.
Accepted:
Published online:
Lucas Fresse 1; Anna Melnikov 2
@article{CRMATH_2011__349_13-14_735_0, author = {Lucas Fresse and Anna Melnikov}, title = {On geometric properties of orbital varieties in type {A}}, journal = {Comptes Rendus. Math\'ematique}, pages = {735--739}, publisher = {Elsevier}, volume = {349}, number = {13-14}, year = {2011}, doi = {10.1016/j.crma.2011.05.016}, language = {en}, }
Lucas Fresse; Anna Melnikov. On geometric properties of orbital varieties in type A. Comptes Rendus. Mathématique, Volume 349 (2011) no. 13-14, pp. 735-739. doi : 10.1016/j.crma.2011.05.016. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2011.05.016/
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