Generic simplicity of quantum Hamiltonian reductions

Akaki Tikaradze

doi:10.5802/crmath.214

Algèbre

Generic simplicity of quantum Hamiltonian reductions

Akaki Tikaradze ¹

¹ University of Toledo, Department of Mathematics & Statistics, Toledo, OH 43606, USA.

Comptes Rendus. Mathématique, Volume 359 (2021) no. 6, pp. 739-742.

Résumé

Let a reductive group $G$ act on a smooth affine complex algebraic variety $X .$ Let $𝔤$ be the Lie algebra of $G$ and $μ : T^{*} (X) \to 𝔤^{*}$ be the moment map. If the moment map is flat, and for a generic character $χ : 𝔤 \to ℂ$ , the action of $G$ on $μ^{- 1} (χ)$ is free, then we show that for very generic characters $χ$ the corresponding quantum Hamiltonian reduction of the ring of differential operators $D (X)$ is simple.

Reçu le : 2020-09-16
Révisé le : 2021-04-01
Accepté le : 2021-04-13
Publié le : 2021-09-02

Zbl

DOI : 10.5802/crmath.214

Affiliations des auteurs :

Akaki Tikaradze ¹

¹ University of Toledo, Department of Mathematics & Statistics, Toledo, OH 43606, USA.

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

@article{CRMATH_2021__359_6_739_0,
     author = {Akaki Tikaradze},
     title = {Generic simplicity of quantum {Hamiltonian} reductions},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {739--742},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {359},
     number = {6},
     year = {2021},
     doi = {10.5802/crmath.214},
     zbl = {07390655},
     language = {en},
}

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Akaki Tikaradze. Generic simplicity of quantum Hamiltonian reductions. Comptes Rendus. Mathématique, Volume 359 (2021) no. 6, pp. 739-742. doi : 10.5802/crmath.214. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.214/

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