The Jacobians and the discriminants of finite reflection groups
type: Item
instance of: scholarly article
title: The Jacobians and the discriminants of finite reflection groups
zbMATH Open document ID: 0679.20042
author: Hiroaki Terao
published in: Tôhoku Mathematical Journal. Second Series
publication date: 1989-01-01T00:00:00Z
review text: Let S be the symmetric algebra of the dual space \(V^*\) of a K-vector space V, G a finite subgroup of GL(V) generated by reflections, \(R=S^ G\) the invariant subring of S under the action of G, and \(Der(S)^ G\) the R-module of G-invariant derivations of Der(S). As the main result in the present paper the author shows: \(Der(S)^ G\simeq D_ R(\delta)\) (as R-modules). Here \(\delta\) is the discriminant of G and \(D_ R(\delta)=\{\theta \in Der(R)|\) \(\theta(\delta)\in \delta R\}\). One of the corollaries of this theorem is: The reflection arrangement A(G) is a free arrangement.
reviewed by: Erich W. Ellers
Mathematics Subject Classification ID: 20H15
Mathematics Subject Classification ID: 51F15
Mathematics Subject Classification ID: 15A72
zbMATH DE Number: 4112888
zbMATH Keywords: finite reflection group
zbMATH Keywords: Jacobian
zbMATH Keywords: symmetric algebra
zbMATH Keywords: invariant subring
zbMATH Keywords: invariant derivations
zbMATH Keywords: discriminant
zbMATH Keywords: reflection arrangement
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2748/tmj/1178227822
OpenAlex ID: W2060706685
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DOI: 10.2748/TMJ/1178227822
description: scientific article; zbMATH DE number 4112888