Some numeric results on root systems
type: Item
instance of: scholarly article
title: Some numeric results on root systems
zbMATH Open document ID: 0738.20047
published in: Pacific Journal of Mathematics
publication date: 1993-01-01T00:00:00Z
review text: Let \(\Phi\) be an irreducible root system. By a subsytem \(\Phi'\) of \(\Phi\), we mean that \(\Phi'\) is a subset of \(\Phi\) which itself forms a root system. Among all subsystems of \(\Phi\), the subsystems of \(\Phi\) of rank 2 and of type \(\neq A_ 1\times A_ 1\) are of particular importance in the theory of Weyl groups and affine Weyl groups. In the present paper, the author computes the number of such subsystems of \(\Phi\) for an irreducible root system \(\Phi\) of any type. Some interesting properties of \(\Phi\) are also obtained.
Mathematics Subject Classification ID: 20G05
Mathematics Subject Classification ID: 20H15
Mathematics Subject Classification ID: 17B20
zbMATH DE Number: 4216127
zbMATH Keywords: irreducible root system
zbMATH Keywords: subsystems
zbMATH Keywords: affine Weyl groups
zbMATH Keywords: reflections in euclidean space
zbMATH Keywords: length of root paths
zbMATH Keywords: number of subsystems
author: Jian-yi Shi
MaRDI profile type: Publication
full work available at URL: pjm.1993.160.155
OpenAlex ID: W2170863865
DOI: 10.2140/PJM.1993.160.155
description: scientific article; zbMATH DE number 4216127