Comptes Rendus
Partial Differential Equations/Complex Analysis
𝒟-modules associated to 3×3 matrices
[𝒟-modules associés aux matrices 3×3]
Comptes Rendus. Mathématique, Volume 338 (2004) no. 2, pp. 139-144.

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.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2003.11.003

Philibert Nang 1

1 Institute of Mathematics, University of Tsukuba, 1-1-1, Tennodai, Tsukuba, Ibaraki, 305-8571, Japan
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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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  • Philibert Nang D-modules on representations of Capelli type, Journal of Algebra, Volume 479 (2017), pp. 380-412 | DOI:10.1016/j.jalgebra.2016.12.029 | Zbl:1372.32016
  • Philibert Nang On the classification of regular holonomic {{\mathcal}} {D}-modules on skew-symmetric matrices, Journal of Algebra, Volume 356 (2012) no. 1, pp. 115-132 | DOI:10.1016/j.jalgebra.2012.01.021 | Zbl:1251.32009
  • Philibert Nang Algebraic description of {{\mathcal}} {D}-modules associated to 3×3 matrices., Bulletin des Sciences Mathématiques, Volume 130 (2006) no. 1, pp. 15-32 | DOI:10.1016/j.bulsci.2005.06.002 | Zbl:1098.32004
  • Philibert Nang {{\mathcal}} {D}-modules associated to the projective space of n×n matrices., Comptes Rendus. Mathématique. Académie des Sciences, Paris, Volume 340 (2005) no. 10, pp. 725-730 | DOI:10.1016/j.crma.2005.04.005 | Zbl:1100.32006
  • Philibert Nang {{{\mathcal}} {D}}-modules associated to the determinantal singularities, Proceedings of the Japan Academy. Series A, Volume 80 (2004) no. 5, pp. 74-78 | DOI:10.3792/pjaa.80.74 | Zbl:1061.32006

Cité par 5 documents. Sources : zbMATH

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