$ \mathcal{D}$-modules associated to 3×3 matrices

Philibert Nang

doi:10.1016/j.crma.2003.11.003

Partial Differential Equations/Complex Analysis

𝒟

-modules associated to 3×3 matrices

Presented by: Masaki Kashiwara

Philibert Nang ¹

¹ Institute of Mathematics, University of Tsukuba, 1-1-1, Tennodai, Tsukuba, Ibaraki, 305-8571, Japan

Comptes Rendus. Mathématique, Volume 338 (2004) no. 2, pp. 139-144.

Abstract (Original language)
Résumé

We classify regular holonomic $𝒟$ -modules whose characteristic variety is contained in the union of conormal bundles to the orbits of the group of invertible matrices. The main result is an equivalence between the category of such $𝒟$ -modules and the one of graded modules of finite type over a Weyl algebra.

On classifie les $𝒟$ -modules holonômes réguliers dont la variéte caractéristique est contenu dans la réunion des fibrés conormaux aux orbites du groupe des matrices inversibles. Le résultat principal est une équivalence entre la catégorie de tels $𝒟$ -modules et celle des modules gradués de type fini sur une algèbre de Weyl.

Received: 2003-08-29
Accepted: 2003-11-04
Published online: 2003-12-09

DOI: 10.1016/j.crma.2003.11.003

Author's affiliations:

Philibert Nang ¹

¹ Institute of Mathematics, University of Tsukuba, 1-1-1, Tennodai, Tsukuba, Ibaraki, 305-8571, Japan

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     author = {Philibert Nang},
     title = {$ \mathcal{D}$-modules associated to 3{\texttimes}3 matrices},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {139--144},
     publisher = {Elsevier},
     volume = {338},
     number = {2},
     year = {2004},
     doi = {10.1016/j.crma.2003.11.003},
     language = {en},
}

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Philibert Nang. $ \mathcal{D}$-modules associated to 3×3 matrices. Comptes Rendus. Mathématique, Volume 338 (2004) no. 2, pp. 139-144. doi : 10.1016/j.crma.2003.11.003. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2003.11.003/

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