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Inverse image of D-modules and quasi-b-functions

In: Algebraic Analysis of Differential Equations

Author

Listed:
  • Yves Laurent

    (Institut Fourier Mathématiques, UMR 5582 CNRS/UJF)

Abstract

The usual b-function of a holonomic $$ \mathcal{D} $$ -module is associated to the Euler vector field but the elementary case of a ramification map shows that this Euler vector field is not preserved under inverse image. We define quasi-b-functions, that is b-functions associated to a quasi-homogeneity and use them to state an inverse image theorem for b-functions of holonomic $$ \mathcal{D} $$ -modules. We apply this result to an explicit calculation of the usual b-function of the Kashiwara-Hotta module on the Grothendieck’s simultaneous resolution of a semi-simple Lie algebra.

Suggested Citation

  • Yves Laurent, 2008. "Inverse image of D-modules and quasi-b-functions," Springer Books, in: Takashi Aoki & Hideyuki Majima & Yoshitsugu Takei & Nobuyuki Tose (ed.), Algebraic Analysis of Differential Equations, pages 167-177, Springer.
    • Handle: RePEc:spr:sprchp:978-4-431-73240-2_16
    DOI: 10.1007/978-4-431-73240-2_16
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