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

Yves Laurent ()
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Yves Laurent: Institut Fourier Mathématiques, UMR 5582 CNRS/UJF

A chapter in Algebraic Analysis of Differential Equations, 2008, pp 167-177 from Springer

Abstract: 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.

Keywords: D-modules; semi-simple Lie groups; b-function (search for similar items in EconPapers)
Date: 2008
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-4-431-73240-2_16

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DOI: 10.1007/978-4-431-73240-2_16

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