$ \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
[

𝒟

-modules associés aux matrices 3×3]

Présenté par : 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 (VO)
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.

Reçu le : 2003-08-29
Accepté le : 2003-11-04
Publié le : 2003-12-09

DOI : 10.1016/j.crma.2003.11.003

Affiliations des auteurs :

Philibert Nang ¹

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

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     title = {$ \mathcal{D}$-modules associated to 3{\texttimes}3 matrices},
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     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/

Bibliographie
Cité par

[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

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 $3 \times 3$ 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 $n \times n$ 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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