Dimension formulas for the hyperfunction solutions of holonomic D-modules

Kiyoshi Takeuchi

doi:10.1016/S0001-8708(02)00099-3

Dimension formulas for the hyperfunction solutions of holonomic D-modules

Kiyoshi Takeuchi

SCI - Mathematics

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

Abstract

In this paper, we will prove an explicit dimension formula for the hyperfunction solutions to a class of holonomic D-modules. This dimension formula can be considered as a higher dimensional analogue of a beautiful theorem on ordinary differential equations due to Kashiwara (Master's Thesis, University of Tokyo, 1970) and Komatsu (J. Fac. Sci. Univ. Tokyo Math. Sect. IA 18 (1971) 379). In the course of the proof, we will make use of a recent innovation of Schmid-Vilonen (Invent. Math. 124 (1996) 451) in the representation theory (in the theory of index theorems for constructible sheaves).

Original language	English
Pages (from-to)	134-145
Number of pages	12
Journal	Advances in Mathematics
Volume	180
Issue number	1
DOIs	https://doi.org/10.1016/S0001-8708(02)00099-3
Publication status	Published - 2003 Dec 1

Keywords

D-module
Holonomic system
Index theorem

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10.1016/S0001-8708(02)00099-3

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AB - In this paper, we will prove an explicit dimension formula for the hyperfunction solutions to a class of holonomic D-modules. This dimension formula can be considered as a higher dimensional analogue of a beautiful theorem on ordinary differential equations due to Kashiwara (Master's Thesis, University of Tokyo, 1970) and Komatsu (J. Fac. Sci. Univ. Tokyo Math. Sect. IA 18 (1971) 379). In the course of the proof, we will make use of a recent innovation of Schmid-Vilonen (Invent. Math. 124 (1996) 451) in the representation theory (in the theory of index theorems for constructible sheaves).

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KW - Holonomic system

KW - Index theorem

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Dimension formulas for the hyperfunction solutions of holonomic D-modules

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Keywords

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