$ \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
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/

References
Cited by

[1] L. Boutet de Monvel D-modules holonômes réguliers en une variable, Mathématiques et Physique, Séminaire de L'ENS, Progr. Math., vol. 37, 1972–1982, pp. 313-321

[2] A. Galligo; M. Granger; P. Maisonobe D-modules et faisceaux pervers dont le support singulier est un croisement normal, I, Ann. Inst. Fourier, Volume 35 (1983) no. 1, pp. 1-48 (II Astérisque, 130, 1985, pp. 240-259)

[3] S.I. Gelfand; S.M. Khoroshkin Algebraic description of certain categories of D-modules, Functionnal. Anal. i Prilozhen., Volume 19 (1985) no. 3, pp. 56-57

[4] M. Kashiwara On the maximal overdetermined systems of linear partial differential equations I, Publ. Res. Inst. Math. Sci., Volume 10 (1975), pp. 563-579

[5] M. Kashiwara On holonomic systems of linear partial differential equations II, Invent. Math., Volume 49 (1978), pp. 121-135

[6] M. Kashiwara Algebraic study of systems of partial differential equations, Mem. Soc. Math. France, Volume 63 (123) (1995) no. 4

[7] M. Kashiwara D-modules and microlocal calculus, Iwanami Series in Modern Mathematics, Transl. Math. Monographs, vol. 217, American Mathematical Society, 2003

[8] M. Kashiwara; T. Kawai On holonomic systems of microdifferential equations III: Systems with regular singularities, Publ. Res. Inst. Math. Sci., Volume 17 (1981), pp. 813-979

[9] R. Macpherson; K. Vilonen Perverse sheaves with regular singularities along the curve xⁿ=yⁿ, Comment. Math. Helv., Volume 63 (1988), pp. 89-102

[10] J. Milnor Singular Points of Complex Hypersurfaces, Annals of Math. Stud., vol. 61, Princeton Univ. Press, 1968

[11] P. Nang D-modules associated to the group of similitudes, Publ. Res. Inst. Math. Sci., Volume 35 (1999) no. 2, pp. 223-247

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