Polyhedra dual to the Weyl chamber decomposition: a précis
type: Item
instance of: scholarly article
title: Polyhedra dual to the Weyl chamber decomposition: a précis
zbMATH Open document ID: 1086.14048
author: Kyoji Saito
published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University
publication date: 2005-07-01T00:00:00Z
review text: From author's abstract: Let \(V_{\mathbb{R}}\) be a real vector space with an irreducible action of a finite reflection group \(W\). The author constructs a one-parameter family of semialgebraic polyhedra \(K_W(\lambda)\) in \(V_\mathbb{R}\) which are dual to the Weyl chamber decomposition of \(V_\mathbb{R}\). The key of such a construction is a theorem on linearization of the tube domain in \((V/\!/W)_\mathbb{R}\) over the simplicial cone. As an application, the author obtains two geometric descriptions of generators for\break \(\pi_1 ((V/\!/W)_\mathbb{C}^{\text{reg}})\), satisfying the Artin braid relations.
reviewed by: Jose Manuel Gamboa
Mathematics Subject Classification ID: 14P10
Mathematics Subject Classification ID: 20F55
zbMATH DE Number: 2185484
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2977/prims/1145475449
OpenAlex ID: W2046122011
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DOI: 10.2977/PRIMS/1145475449
description: scientific article; zbMATH DE number 2185484