Counting one-codimensional subspaces generated by subsets of a root system
type: Item
instance of: scholarly article
zbMATH Open document ID: 1257.17014
author: Tomohiro Kamiyoshi
author: Makoto Nagura
author: Shin-Ichi Otani
publication date: 2012-07-20T00:00:00Z
full work available at URL: index.html
Mathematics Subject Classification ID: 17B22
Mathematics Subject Classification ID: 15A21
Mathematics Subject Classification ID: 11S90
zbMATH DE Number: 6058639
zbMATH Keywords: root system
zbMATH Keywords: semisimple finite prehomogeneous vector space
MaRDI profile type: Publication
title: Counting one-codimensional subspaces generated by subsets of a root system
published in: International Journal of Algebra
review text: Let \(\Phi\) be an irreducible reduced root system in a Euclidean space \(E\). The authors give a complete classification of one-codimensional subspaces of \(E\) generated by subsets of \(\Phi\). A basis for each such subspace is given explicitly for the classical types. For exceptional types (except \(G_2\)), the calculations are done using computer. The paper is concluded with an application to the classification theory of semisimple finite prehomogeneous vector spaces.
reviewed by: Saeid Azam
description: scientific article; zbMATH DE number 6058639