Regular elements and monodromy of discriminants of finite reflection groups
type: Item
instance of: scholarly article
title: Regular elements and monodromy of discriminants of finite reflection groups
zbMATH Open document ID: 0832.32019
DOI: 10.1016/0019-3577(95)91238-Q
published in: Indagationes Mathematicae. New Series
publication date: 1995-09-04T00:00:00Z
review text: Let \(G \subseteq GL_n (\mathbb{C})\) be a finite subgroup generated by reflections. For each reflection hyperplane \(H\) of \(G\) let \(\ell_H : \mathbb{C}^n \to \mathbb{C}\) be a linear form defining \(H\) and \(e(H)\) the order of the subgroup of elements of \(G\) which fix \(H\) pointwise. Let \(\delta = \prod_H \ell_H^{e(H)}\) and \(\Delta : \mathbb{C}^n/G \to \mathbb{C}\) the map induced by \(\delta\). Let \(Z(T,G)\) be the zeta function of the local monodromy of \(\Delta\) at 0. This zeta function is calculated case by case for all irreducible finite reflection groups \(G\).
reviewed by: Gerhard Pfister
Mathematics Subject Classification ID: 32S40
Mathematics Subject Classification ID: 14B05
Mathematics Subject Classification ID: 20H15
zbMATH DE Number: 792820
zbMATH Keywords: zeta function
zbMATH Keywords: monodromy
zbMATH Keywords: finite reflection groups
author: Jan Denef
author: François Loeser
MaRDI profile type: Publication
cites work: Q3994029
cites work: Resolution of Singularities and Division of Distributions
cites work: Q5580319
cites work: Finite complex reflection groups
cites work: Q4285665
cites work: MACDONALD INTEGRALS AND MONODROMY
cites work: Invariants of finite reflection groups
cites work: Cohomology of the commutator subgroup of the braid group
cites work: Q3998721
cites work: Arrangements d'hyperplans et sommes de Gauss
cites work: Finite difference equations and determinants of integrals of multiform functions
cites work: Some Conjectures for Root Systems
cites work: Q3310138
cites work: Singular Points of Complex Hypersurfaces. (AM-61)
cites work: Some applications of hypergeometric shift operators
cites work: Unitary reflection groups and cohomology
cites work: Discriminants in the invariant theory of reflection groups
cites work: Q4003206
cites work: Finite Unitary Reflection Groups
cites work: Regular elements of finite reflection groups
cites work: Q3966260
cites work: Q3338538
cites work: The microlocal structure of weighted homogeneous polynomials associated with the Coxeter systems
full work available at URL: 0019-3577(95)91238-q
OpenAlex ID: W2023782559
description: scientific article; zbMATH DE number 792820